Large-Scale Data Processing with MapReduce

Large-Scale Data Processing with MapReduce

SIKS/BigGrid Big Data Tutorial

Jimmy LinUniversity of Maryland

Nov. 30 & Dec. 1, 2011

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United StatesSee http://creativecommons.org/licenses/by-nc-sa/3.0/us/ for details

These slides are available on my homepage at http://www.umiacs.umd.edu/~jimmylin/

First things first… About me Course history Audience survey

Agenda Today:

Setting the stage: Why large data? Why is this different? Introduction to MapReduce MapReduce algorithm design Hadoop ecosystem tour

Tomorrow: Text retrieval Managing relational data Graph algorithms

Expectations Focus on “thinking at scale” Deconstruction into “design patterns” Basic intuitions, not fancy math Mapping well-known algorithms to MapReduce Not a tutorial on programming Hadoop Entry point to book

Setting the Stage:

Why large data?

Setting the stageIntroduction to MapReduceMapReduce algorithm designHadoop ecosystem tourText retrievalManaging relational dataGraph algorithms

Source: Wikipedia (Everest)

How much data?

9 PB of user data +>50 TB/day (11/2011)

processes 20 PB a day (2008)

36 PB of user data + 80-90 TB/day (6/2010)

Wayback Machine: 3 PB + 100 TB/month (3/2009)

LHC: ~15 PB a year(at full capacity)

LSST: 6-10 PB a year (~2015)

640K ought to be enough for anybody.

150 PB on 50k+ servers running 15k apps

S3: 449B objects, peak 290k request/second (7/2011)

No data like more data!

(Banko and Brill, ACL 2001)(Brants et al., EMNLP 2007)

s/knowledge/data/g;

How do we get here if we’re not Google?

+ simple, distributed programming models cheap commodity clusters

= data-intensive computing for the masses!

Setting the Stage:

Why is this different?


Parallel computing is hard!

Message Passing

P1 P2 P3 P4 P5

Shared Memory

P1 P2 P3 P4 P5

Mem

ory

Different programming models

Different programming constructsmutexes, conditional variables, barriers, …masters/slaves, producers/consumers, work queues, …

Fundamental issuesscheduling, data distribution, synchronization, inter-process communication, robustness, fault tolerance, …

Common problemslivelock, deadlock, data starvation, priority inversion…dining philosophers, sleeping barbers, cigarette smokers, …

Architectural issuesFlynn’s taxonomy (SIMD, MIMD, etc.),network typology, bisection bandwidthUMA vs. NUMA, cache coherence

The reality: programmer shoulders the burden of managing concurrency…(I want my students developing new algorithms, not debugging race conditions)

master

slaves

producer consumer

producer consumer

work queue

Where the rubber meets the road Concurrency is difficult to reason about

At the scale of datacenters (even across datacenters) In the presence of failures In terms of multiple interacting services

The reality: Lots of one-off solutions, custom code Write you own dedicated library, then program with it Burden on the programmer to explicitly manage everything

Source: Ricardo Guimarães Herrmann

Source: NY Times (6/14/2006)

The datacenter is the computer!

I think there is a world market for about five computers.

What’s the point? It’s all about the right level of abstraction Hide system-level details from the developers

No more race conditions, lock contention, etc. Separating the what from how

Developer specifies the computation that needs to be performed Execution framework (“runtime”) handles actual execution

The datacenter is the computer!

“Big Ideas” Scale “out”, not “up”

Limits of SMP and large shared-memory machines Move processing to the data

Cluster have limited bandwidth Process data sequentially, avoid random access

Seeks are expensive, disk throughput is reasonable Seamless scalability

From the mythical man-month to the tradable machine-hour

Building Blocks

Source: Barroso and Urs Hölzle (2009)

Storage Hierarchy

Funny story about sense of scale…Source: Barroso and Urs Hölzle (2009)

Storage Hierarchy


Anatomy of a Datacenter


Source: www.robinmajumdar.com

Source: Harper’s (Feb, 2008)

Source: Wikipedia (The Dalles, Oregon)

Source: Bonneville Power Administration

Introduction to MapReduce


Typical Large-Data Problem Iterate over a large number of records Extract something of interest from each Shuffle and sort intermediate results Aggregate intermediate results Generate final output

Key idea: provide a functional abstraction for these two operations

Map

Reduce

(Dean and Ghemawat, OSDI 2004)

g g g g g

f f f f fMap

Fold

Roots in Functional Programming

MapReduce Programmers specify two functions:

map (k, v) → <k’, v’>*reduce (k’, v’) → <k’, v’>* All values with the same key are sent to the same reducer

The execution framework handles everything else…

mapmap map map

Shuffle and Sort: aggregate values by keys

reduce reduce reduce

k1 k2 k3 k4 k5 k6v1 v2 v3 v4 v5 v6

ba 1 2 c c3 6 a c5 2 b c7 8

a 1 5 b 2 7 c 2 3 6 8

r1 s1 r2 s2 r3 s3


map (k, v) → <k’, v’>*reduce (k’, v’) → <k’, v’>* All values with the same key are sent to the same reducer


What’s “everything else”?

MapReduce “Runtime” Handles scheduling

Assigns workers to map and reduce tasks Handles “data distribution”

Moves processes to data Handles synchronization

Gathers, sorts, and shuffles intermediate data Handles errors and faults

Detects worker failures and restarts Everything happens on top of a distributed FS


map (k, v) → <k’, v’>*reduce (k’, v’) → <k’, v’>* All values with the same key are reduced together

The execution framework handles everything else… Not quite…usually, programmers also specify:

partition (k’, number of partitions) → partition for k’ Often a simple hash of the key, e.g., hash(k’) mod n Divides up key space for parallel reduce operationscombine (k’, v’) → <k’, v’>* Mini-reducers that run in memory after the map phase Used as an optimization to reduce network traffic

combinecombine combine combine

ba 1 2 c 9 a c5 2 b c7 8

partition partition partition partition

mapmap map map

k1 k2 k3 k4 k5 k6v1 v2 v3 v4 v5 v6

ba 1 2 c c3 6 a c5 2 b c7 8



a 1 5 b 2 7 c 2 9 8

r1 s1 r2 s2 r3 s3

c 2 3 6 8

Two more details… Barrier between map and reduce phases

But we can begin copying intermediate data earlier Keys arrive at each reducer in sorted order

No enforced ordering across reducers

“Hello World”: Word Count

MapReduce can refer to… The programming model The execution framework (aka “runtime”) The specific implementation

Usage is usually clear from context!

MapReduce Implementations Google has a proprietary implementation in C++

Bindings in Java, Python Hadoop is an open-source implementation in Java

Original development led by Yahoo Now an Apache open source project Emerging as the de facto big data stack Rapidly expanding software ecosystem

Lots of custom research implementations For GPUs, cell processors, etc. Includes variations of the basic programming model

Most of these slides are focused on Hadoop

split 0split 1split 2split 3split 4

worker

worker

worker

worker

worker

Master

UserProgram

outputfile 0

outputfile 1

(1) submit

(2) schedule map (2) schedule reduce

(3) read(4) local write

(5) remote read(6) write

Inputfiles

Mapphase

Intermediate files(on local disk)

Reducephase

Outputfiles

Adapted from (Dean and Ghemawat, OSDI 2004)

How do we get data to the workers?

Compute Nodes

NAS

SAN

What’s the problem here?

Distributed File System Don’t move data to workers… move workers to the data!

Store data on the local disks of nodes in the cluster Start up the workers on the node that has the data local

A distributed file system is the answer GFS (Google File System) for Google’s MapReduce HDFS (Hadoop Distributed File System) for Hadoop

GFS: Assumptions Commodity hardware over “exotic” hardware

Scale “out”, not “up” High component failure rates

Inexpensive commodity components fail all the time “Modest” number of huge files

Multi-gigabyte files are common, if not encouraged Files are write-once, mostly appended to

Perhaps concurrently Large streaming reads over random access

High sustained throughput over low latency

GFS slides adapted from material by (Ghemawat et al., SOSP 2003)

GFS: Design Decisions Files stored as chunks

Fixed size (64MB) Reliability through replication

Each chunk replicated across 3+ chunkservers Single master to coordinate access, keep metadata

Simple centralized management No data caching

Little benefit due to large datasets, streaming reads Simplify the API

Push some of the issues onto the client (e.g., data layout)

HDFS = GFS clone (same basic ideas)

From GFS to HDFS Terminology differences:

GFS master = Hadoop namenode GFS chunkservers = Hadoop datanodes

Functional differences: File appends in HDFS is relatively new HDFS performance is (likely) slower

For the most part, we’ll use the Hadoop terminology…

Adapted from (Ghemawat et al., SOSP 2003)

(file name, block id)

(block id, block location)

instructions to datanode

datanode state(block id, byte range)

block data

HDFS namenode

HDFS datanode

Linux file system

…

HDFS datanode

Linux file system

…

File namespace/foo/bar

block 3df2

Application

HDFS Client

HDFS Architecture

Namenode Responsibilities Managing the file system namespace:

Holds file/directory structure, metadata, file-to-block mapping, access permissions, etc.

Coordinating file operations: Directs clients to datanodes for reads and writes No data is moved through the namenode

Maintaining overall health: Periodic communication with the datanodes Block re-replication and rebalancing Garbage collection

Putting everything together…

datanode daemon

Linux file system

…

tasktracker

slave node

datanode daemon

Linux file system

…

tasktracker

slave node

datanode daemon

Linux file system

…

tasktracker

slave node

namenode

namenode daemon

job submission node

jobtracker

MapReduce Algorithm Design


MapReduce: Recap Programmers must specify:

map (k, v) → <k’, v’>*reduce (k’, v’) → <k’, v’>* All values with the same key are reduced together

Optionally, also:partition (k’, number of partitions) → partition for k’ Often a simple hash of the key, e.g., hash(k’) mod n Divides up key space for parallel reduce operationscombine (k’, v’) → <k’, v’>* Mini-reducers that run in memory after the map phase Used as an optimization to reduce network traffic


combinecombine combine combine

ba 1 2 c 9 a c5 2 b c7 8

partition partition partition partition

mapmap map map

k1 k2 k3 k4 k5 k6v1 v2 v3 v4 v5 v6

ba 1 2 c c3 6 a c5 2 b c7 8



a 1 5 b 2 7 c 2 9 8

r1 s1 r2 s2 r3 s3

“Everything Else” The execution framework handles everything else…

Scheduling: assigns workers to map and reduce tasks “Data distribution”: moves processes to data Synchronization: gathers, sorts, and shuffles intermediate data Errors and faults: detects worker failures and restarts

Limited control over data and execution flow All algorithms must expressed in m, r, c, p

You don’t know: Where mappers and reducers run When a mapper or reducer begins or finishes Which input a particular mapper is processing Which intermediate key a particular reducer is processing

Tools for Synchronization Cleverly-constructed data structures

Bring partial results together Sort order of intermediate keys

Control order in which reducers process keys Partitioner

Control which reducer processes which keys Preserving state in mappers and reducers

Capture dependencies across multiple keys and values

Designing Scalable Algorithms Ideal scaling characteristics:

Twice the data, twice the running time Twice the resources, half the running time

Running time: Anything more than linear algorithms won’t scale Constants matter (more than you think)*

* But, Knuth’s advice should still be heeded.

Scalable Hadoop Algorithms: Themes Avoid object creation

Inherently costly operation Garbage collection

Avoid buffering Limited heap size Works for small datasets, but won’t scale!

Avoid communication Reduce cross-node dependencies via local aggregation Combiners can help… but even better approaches available

Shuffle and Sort

Mapper

Reducer

other mappers

other reducers

circular buffer (in memory)

spills (on disk)

merged spills (on disk)

intermediate files (on disk)

Combiner

Combiner

Word Count: Baseline

What’s the impact of combiners?

Word Count: Version 1

Are combiners still needed?

Preserving State

Mapper object

configure

map

close

stateone object per task

Reducer object

configure

reduce

close

state

one call per input key-value pair

one call per intermediate key

API initialization hook

API cleanup hook

Word Count: Version 2


Key: preserve state across

input key-value pairs!

Design Pattern for Local Aggregation “In-mapper combining”

Fold the functionality of the combiner into the mapper by preserving state across multiple map calls

Advantages Speed Why is this faster than actual combiners?

Disadvantages Explicit memory management required Potential for order-dependent bugs

Combiner Design Combiners and reducers share same method signature

Sometimes, reducers can serve as combiners Often, not…

Remember: combiner are optional optimizations Should not affect algorithm correctness May be run 0, 1, or multiple times

Example: find average of all integers associated with the same key

Computing the Mean: Version 1

Why can’t we use reducer as combiner?


Why doesn’t this work?


Fixed?

“Count and Normalize” Many algorithms reduce to estimating relative frequencies:

In the case of EM, pseudo-counts instead of actual counts For a large class of algorithms: intuition is the same, just

varying complexity in terms of bookkeeping Let’s start with the intuition…

'

)',(count),(count

)(count),(count)|(

B

BABA

ABAABf

Algorithm Design: Running Example Term co-occurrence matrix for a text collection

M = N x N matrix (N = vocabulary size) Mij: number of times i and j co-occur in some context

(for concreteness, let’s say context = sentence) Why?

Distributional profiles as a way of measuring semantic distance Semantic distance useful for many language processing tasks

MapReduce: Large Counting Problems Term co-occurrence matrix for a text collection

= specific instance of a large counting problem A large event space (number of terms) A large number of observations (the collection itself) Goal: keep track of interesting statistics about the events

Basic approach Mappers generate partial counts Reducers aggregate partial counts

How do we aggregate partial counts efficiently?

First Try: “Pairs” Each mapper takes a sentence:

Generate all co-occurring term pairs For all pairs, emit (a, b) → count

Reducers sum up counts associated with these pairs Use combiners!

Pairs: Pseudo-Code

“Pairs” Analysis Advantages

Easy to implement, easy to understand Disadvantages

Lots of pairs to sort and shuffle around (upper bound?) Not many opportunities for combiners to work

Another Try: “Stripes” Idea: group together pairs into an associative array

Each mapper takes a sentence: Generate all co-occurring term pairs For each term, emit a → { b: countb, c: countc, d: countd … }

Reducers perform element-wise sum of associative arrays

(a, b) → 1 (a, c) → 2 (a, d) → 5 (a, e) → 3 (a, f) → 2

a → { b: 1, c: 2, d: 5, e: 3, f: 2 }

a → { b: 1, d: 5, e: 3 }a → { b: 1, c: 2, d: 2, f: 2 }a → { b: 2, c: 2, d: 7, e: 3, f: 2 }

+

Key: cleverly-constructed data structure

brings together partial results

Stripes: Pseudo-Code

“Stripes” Analysis Advantages

Far less sorting and shuffling of key-value pairs Can make better use of combiners

Disadvantages More difficult to implement Underlying object more heavyweight Fundamental limitation in terms of size of event space

Cluster size: 38 coresData Source: Associated Press Worldstream (APW) of the English Gigaword Corpus (v3), which contains 2.27 million documents (1.8 GB compressed, 5.7 GB uncompressed)

Relative Frequencies How do we estimate relative frequencies from counts?

Why do we want to do this? How do we do this with MapReduce?

'

)',(count),(count

)(count),(count)|(

B

BABA

ABAABf

f(B|A): “Stripes”

Easy! One pass to compute (a, *) Another pass to directly compute f(B|A)

a → {b1:3, b2 :12, b3 :7, b4 :1, … }

f(B|A): “Pairs”

For this to work: Must emit extra (a, *) for every bn in mapper Must make sure all a’s get sent to same reducer (use partitioner) Must make sure (a, *) comes first (define sort order) Must hold state in reducer across different key-value pairs

(a, b1) → 3 (a, b2) → 12 (a, b3) → 7(a, b4) → 1 …

(a, *) → 32

(a, b1) → 3 / 32 (a, b2) → 12 / 32(a, b3) → 7 / 32(a, b4) → 1 / 32…

Reducer holds this value in memory

“Order Inversion” Common design pattern

Computing relative frequencies requires marginal counts But marginal cannot be computed until you see all counts Buffering is a bad idea! Trick: getting the marginal counts to arrive at the reducer before

the joint counts Optimizations

Apply in-memory combining pattern to accumulate marginal counts Should we apply combiners?

Synchronization: Pairs vs. Stripes Approach 1: turn synchronization into an ordering problem

Sort keys into correct order of computation Partition key space so that each reducer gets the appropriate set

of partial results Hold state in reducer across multiple key-value pairs to perform

computation Illustrated by the “pairs” approach

Approach 2: construct data structures that bring partial results together Each reducer receives all the data it needs to complete the

computation Illustrated by the “stripes” approach

Secondary Sorting MapReduce sorts input to reducers by key

Values may be arbitrarily ordered What if want to sort value also?

E.g., k → (v1, r), (v3, r), (v4, r), (v8, r)…

Secondary Sorting: Solutions Solution 1:

Buffer values in memory, then sort Why is this a bad idea?

Solution 2: “Value-to-key conversion” design pattern: form composite

intermediate key, (k, v1) Let execution framework do the sorting Preserve state across multiple key-value pairs to handle

processing Anything else we need to do?

Recap: Tools for Synchronization Cleverly-constructed data structures

Bring data together Sort order of intermediate keys

Control order in which reducers process keys Partitioner

Control which reducer processes which keys Preserving state in mappers and reducers

Capture dependencies across multiple keys and values

Issues and Tradeoffs Number of key-value pairs

Object creation overhead Time for sorting and shuffling pairs across the network

Size of each key-value pair De/serialization overhead

Local aggregation Opportunities to perform local aggregation varies Combiners make a big difference Combiners vs. in-mapper combining RAM vs. disk vs. network

Hadoop Ecosystem Tour


From GFS to Bigtable Google’s GFS is a distributed file system Bigtable is a storage system for structured data

Built on top of GFS Solves many GFS issues: real-time access, short files, short reads Serves as a source and a sink for MapReduce jobs

Bigtable: Data Model A table is a sparse, distributed, persistent

multidimensional sorted map Map indexed by a row key, column key, and a timestamp

(row:string, column:string, time:int64) uninterpreted byte array Supports lookups, inserts, deletes

Single row transactions only

Image Source: Chang et al., OSDI 2006

HBase

Image Source: http://www.larsgeorge.com/2009/10/hbase-architecture-101-storage.html


The datacenter is the computer!It’s all about the right level of abstraction

Need for High-Level Languages Hadoop is great for large-data processing!

But writing Java programs for everything is verbose and slow Analysts don’t want to (or can’t) write Java

Solution: develop higher-level data processing languages Hive: HQL is like SQL Pig: Pig Latin is a dataflow language

Hive and Pig Hive: data warehousing application in Hadoop

Query language is HQL, variant of SQL Tables stored on HDFS as flat files Developed by Facebook, now open source

Pig: large-scale data processing system Scripts are written in Pig Latin, a dataflow language Developed by Yahoo!, now open source Roughly 1/3 of all Yahoo! internal jobs

Common idea: Provide higher-level language to facilitate large-data processing Higher-level language “compiles down” to Hadoop jobs

Hive: Example Hive looks similar to an SQL database Relational join on two tables:

Table of word counts from Shakespeare collection Table of word counts from the bible

Source: Material drawn from Cloudera training VM

SELECT s.word, s.freq, k.freq FROM shakespeare s JOIN bible k ON (s.word = k.word) WHERE s.freq >= 1 AND k.freq >= 1 ORDER BY s.freq DESC LIMIT 10;

the 25848 62394I 23031 8854and 19671 38985to 18038 13526of 16700 34654a 14170 8057you 12702 2720my 11297 4135in 10797 12445is 8882 6884

Hive: Behind the ScenesSELECT s.word, s.freq, k.freq FROM shakespeare s JOIN bible k ON (s.word = k.word) WHERE s.freq >= 1 AND k.freq >= 1 ORDER BY s.freq DESC LIMIT 10;

(TOK_QUERY (TOK_FROM (TOK_JOIN (TOK_TABREF shakespeare s) (TOK_TABREF bible k) (= (. (TOK_TABLE_OR_COL s) word) (. (TOK_TABLE_OR_COL k) word)))) (TOK_INSERT (TOK_DESTINATION (TOK_DIR TOK_TMP_FILE)) (TOK_SELECT (TOK_SELEXPR (. (TOK_TABLE_OR_COL s) word)) (TOK_SELEXPR (. (TOK_TABLE_OR_COL s) freq)) (TOK_SELEXPR (. (TOK_TABLE_OR_COL k) freq))) (TOK_WHERE (AND (>= (. (TOK_TABLE_OR_COL s) freq) 1) (>= (. (TOK_TABLE_OR_COL k) freq) 1))) (TOK_ORDERBY (TOK_TABSORTCOLNAMEDESC (. (TOK_TABLE_OR_COL s) freq))) (TOK_LIMIT 10)))

(one or more of MapReduce jobs)

(Abstract Syntax Tree)

Hive: Behind the ScenesSTAGE DEPENDENCIES: Stage-1 is a root stage Stage-2 depends on stages: Stage-1 Stage-0 is a root stage

STAGE PLANS: Stage: Stage-1 Map Reduce Alias -> Map Operator Tree: s TableScan alias: s Filter Operator predicate: expr: (freq >= 1) type: boolean Reduce Output Operator key expressions: expr: word type: string sort order: + Map-reduce partition columns: expr: word type: string tag: 0 value expressions: expr: freq type: int expr: word type: string k TableScan alias: k Filter Operator predicate: expr: (freq >= 1) type: boolean Reduce Output Operator key expressions: expr: word type: string sort order: + Map-reduce partition columns: expr: word type: string tag: 1 value expressions: expr: freq type: int

Reduce Operator Tree: Join Operator condition map: Inner Join 0 to 1 condition expressions: 0 {VALUE._col0} {VALUE._col1} 1 {VALUE._col0} outputColumnNames: _col0, _col1, _col2 Filter Operator predicate: expr: ((_col0 >= 1) and (_col2 >= 1)) type: boolean Select Operator expressions: expr: _col1 type: string expr: _col0 type: int expr: _col2 type: int outputColumnNames: _col0, _col1, _col2 File Output Operator compressed: false GlobalTableId: 0 table: input format: org.apache.hadoop.mapred.SequenceFileInputFormat output format: org.apache.hadoop.hive.ql.io.HiveSequenceFileOutputFormat

Stage: Stage-2 Map Reduce Alias -> Map Operator Tree: hdfs://localhost:8022/tmp/hive-training/364214370/10002 Reduce Output Operator key expressions: expr: _col1 type: int sort order: - tag: -1 value expressions: expr: _col0 type: string expr: _col1 type: int expr: _col2 type: int Reduce Operator Tree: Extract Limit File Output Operator compressed: false GlobalTableId: 0 table: input format: org.apache.hadoop.mapred.TextInputFormat output format: org.apache.hadoop.hive.ql.io.HiveIgnoreKeyTextOutputFormat

Stage: Stage-0 Fetch Operator limit: 10

Pig: Example

User Url Time

Amy cnn.com 8:00

Amy bbc.com 10:00

Amy flickr.com 10:05

Fred cnn.com 12:00

Url Category PageRank

cnn.com News 0.9

bbc.com News 0.8

flickr.com Photos 0.7

espn.com Sports 0.9

Visits Url Info

Task: Find the top 10 most visited pages in each category

Pig Slides adapted from Olston et al. (SIGMOD 2008)

Pig Query Plan

Load Visits

Group by url

Foreach urlgenerate count Load Url Info

Join on url

Group by category

Foreach categorygenerate top10(urls)


Pig Script

visits = load ‘/data/visits’ as (user, url, time);gVisits = group visits by url;visitCounts = foreach gVisits generate url, count(visits);urlInfo = load ‘/data/urlInfo’ as (url, category, pRank);visitCounts = join visitCounts by url, urlInfo by url;gCategories = group visitCounts by category;topUrls = foreach gCategories generate top(visitCounts,10);

store topUrls into ‘/data/topUrls’;


Load Visits

Group by url

Foreach urlgenerate count Load Url Info

Join on url

Group by category

Foreach categorygenerate top10(urls)

Pig Script in HadoopMap1

Reduce1 Map2

Reduce2

Map3

Reduce3


Text Retrieval


Abstract IR Architecture

DocumentsQuery

Hits

RepresentationFunction

RepresentationFunction

Query Representation Document Representation

ComparisonFunction Index

offlineonlinedocument acquisition

(e.g., web crawling)

“Bag of Words” Terms weights computed as functions of:

Term frequency Collection frequency Document frequency Average document length …

Well-known weighting functions TF.IDF BM25 Dirichlet scores (LM framework)

Similarity boils down to inner products of feature vectors:

n

i kijikjkj wwddddsim1 ,,),(

2

1

1

2

1

1

1

1

1

1

1

Inverted Index

2

1

2

1

1

1

1 2 3

1

1

1

4

1

1

1

1

1

1

2

1

tfdf

blue

cat

egg

fish

green

ham

hat

one

1

1

1

1

1

1

2

1

blue

cat

egg

fish

green

ham

hat

one

1 1red

1 1two

1red

1two

one fish, two fishDoc 1

red fish, blue fishDoc 2

cat in the hatDoc 3

green eggs and hamDoc 4

3

4

1

4

4

3

2

1

2

2

1

[2,4]

[3]

[2,4]

[2]

[1]

[1]

[3]

[2]

[1]

[1]

[3]

2

1

1

2

1

1

1

1

1

1

1

Inverted Index: Positional Information

2

1

2

1

1

1

1 2 3

1

1

1

4

1

1

1

1

1

1

2

1

tfdf

blue

cat

egg

fish

green

ham

hat

one

1

1

1

1

1

1

2

1

blue

cat

egg

fish

green

ham

hat

one

1 1red

1 1two

1red

1two



cat in the hatDoc 3

green eggs and hamDoc 4

3

4

1

4

4

3

2

1

2

2

1

Retrieval in a Nutshell Look up postings lists corresponding to query terms Traverse postings for each query term Store partial query-document scores in accumulators Select top k results to return

Retrieval: Document-at-a-Time Evaluate documents one at a time (score all query terms)

Tradeoffs Small memory footprint (good) Must read through all postings (bad), but skipping possible More disk seeks (bad), but blocking possible

fish 2 1 3 1 2 31 9 21 34 35 80 …

blue 2 1 19 21 35 …

Accumulators(e.g. priority queue)

Document score in top k?Yes: Insert document score, extract-min if queue too largeNo: Do nothing

Retrieval: Term-at-a-Time Evaluate documents one query term at a time

Usually, starting from most rare term (often with tf-sorted postings)

Tradeoffs Early termination heuristics (good) Large memory footprint (bad), but filtering heuristics possible

fish 2 1 3 1 2 31 9 21 34 35 80 …

blue 2 1 19 21 35 …Accumulators

(e.g., hash)Score{q=x}(doc n) = s

MapReduce it? The indexing problem

Scalability is critical Must be relatively fast, but need not be real time Fundamentally a batch operation Incremental updates may or may not be important For the web, crawling is a challenge in itself

The retrieval problem Must have sub-second response time For the web, only need relatively few results

Perfect for MapReduce!

Uh… not so good…

Indexing: Performance Analysis Fundamentally, a large sorting problem

Terms usually fit in memory Postings usually don’t

How is it done on a single machine? How can it be done with MapReduce? First, let’s characterize the problem size:

Size of vocabulary Size of postings

Vocabulary Size: Heaps’ Law

Heaps’ Law: linear in log-log space Vocabulary size grows unbounded!

bkTM M is vocabulary sizeT is collection size (number of documents)k and b are constants

Typically, k is between 30 and 100, b is between 0.4 and 0.6

Heaps’ Law for RCV1

Reuters-RCV1 collection: 806,791 newswire documents (Aug 20, 1996-August 19, 1997)

k = 44b = 0.49

First 1,000,020 terms: Predicted = 38,323 Actual = 38,365

Manning, Raghavan, Schütze, Introduction to Information Retrieval (2008)

Postings Size: Zipf’s Law

Zipf’s Law: (also) linear in log-log space Specific case of Power Law distributions

In other words: A few elements occur very frequently Many elements occur very infrequently

ic

i cf cf is the collection frequency of i-th common termc is a constant

Zipf’s Law for RCV1

Reuters-RCV1 collection: 806,791 newswire documents (Aug 20, 1996-August 19, 1997)

Fit isn’t that good… but good enough!

Manning, Raghavan, Schütze, Introduction to Information Retrieval (2008)

MapReduce: Index Construction Map over all documents

Emit term as key, (docno, tf) as value Emit other information as necessary (e.g., term position)

Sort/shuffle: group postings by term Reduce

Gather and sort the postings (e.g., by docno or tf) Write postings to disk

MapReduce does all the heavy lifting!

1

1

2

1

1

2 2

11

1

11

1

1

1

2

Inverted Indexing with MapReduce

1one

1two

1fish


2red

2blue

2fish


3cat

3hat

cat in the hatDoc 3

1fish 2

1one1two

2red

3cat2blue

3hat


Map

Reduce

Inverted Indexing: Pseudo-Code

[2,4]

[1]

[3]

[1]

[2]

[1]

[1]

[3]

[2]

[3][2,4]

[1]

[2,4]

[2,4]

[1]

[3]

1

1

2

1

1

2

1

1

2 2

11

1

11

1

Positional Indexes

1one

1two

1fish

2red

2blue

2fish

3cat

3hat

1fish 2

1one1two

2red

3cat2blue

3hat


Map

Reduce



cat in the hatDoc 3

Inverted Indexing: Pseudo-Code

What’s the problem?

Scalability Bottleneck Initial implementation: terms as keys, postings as values

Reducers must buffer all postings associated with key (to sort) What if we run out of memory to buffer postings?

Uh oh!

[2,4]

[9]

[1,8,22]

[23]

[8,41]

[2,9,76]

[2,4]

[9]

[1,8,22]

[23]

[8,41]

[2,9,76]

2

1

3

1

2

3

Another Try…

1fish

9

21

(values)(key)

34

35

80

1fish

9

21

(values)(keys)

34

35

80

fish

fish

fish

fish

fish

How is this different?• Let the framework do the sorting• Term frequency implicitly stored• Directly write compressed postings

Where have we seen this before?

2 1 3 1 2 3

2 1 3 1 2 3

Postings Encoding

1fish 9 21 34 35 80 …

1fish 8 12 13 1 45 …

Conceptually:

In Practice:

• Don’t encode docnos, encode gaps (or d-gaps) • But it’s not obvious that this save space…

Overview of Index Compression Byte-aligned vs. bit-aligned Non-parameterized bit-aligned

Unary codes codes codes

Parameterized bit-aligned Golomb codes (local Bernoulli model)

Block-based methods Simple-9 PForDelta

Want more detail? Start with Managing Gigabytes by Witten, Moffat, and Bell!

Index Compression: Performance

Witten, Moffat, Bell, Managing Gigabytes (1999)

Unary 262 1918

Binary 15 20 6.51 6.63 6.23 6.38

Golomb 6.09 5.84

Bible TREC

Bible: King James version of the Bible; 31,101 verses (4.3 MB)TREC: TREC disks 1+2; 741,856 docs (2070 MB)

One common approach

Comparison of Index Size (bits per pointer)

Issue: For Golomb compression, optimal b ~ 0.69 (N/df)Which means different b for every term!

Chicken and Egg?

1fish

9

[2,4]

[9]

21 [1,8,22]

(value)(key)

34 [23]

35 [8,41]

80 [2,9,76]

fish

fish

fish

fish

fish

Write directly to disk

But wait! How do we set the Golomb parameter b?

We need the df to set b…

But we don’t know the df until we’ve seen all postings!

…

Optimal b ~ 0.69 (N/df)

Sound familiar?

Getting the df In the mapper:

Emit “special” key-value pairs to keep track of df In the reducer:

Make sure “special” key-value pairs come first: process them to determine df

Remember: proper partitioning!

Getting the df: Modified Mapper


1fish [2,4]

(value)(key)

1one [1]

1two [3]

fish [1]

one [1]

two [1]

Input document…

Emit normal key-value pairs…

Emit “special” key-value pairs to keep track of df…

Getting the df: Modified Reducer

1fish

9

[2,4]

[9]

21 [1,8,22]

(value)(key)

34 [23]

35 [8,41]

80 [2,9,76]

fish

fish

fish

fish

fishWrite compressed postings

fish [63] [82] [27] …

…

First, compute the df by summing contributions from all “special” key-value pair…

Compute Golomb parameter b…

Important: properly define sort order to make sure “special” key-value pairs come first!

Where have we seen this before?

MapReduce it? The indexing problem

Scalability is paramount Must be relatively fast, but need not be real time Fundamentally a batch operation Incremental updates may or may not be important For the web, crawling is a challenge in itself

The retrieval problem Must have sub-second response time For the web, only need relatively few results

Retrieval with MapReduce? MapReduce is fundamentally batch-oriented

Optimized for throughput, not latency Startup of mappers and reducers is expensive

MapReduce is not suitable for real-time queries! Use separate infrastructure for retrieval…

Important Ideas Partitioning (for scalability) Replication (for redundancy) Caching (for speed) Routing (for load balancing)

The rest is just details!

Term vs. Document Partitioning

…

T

DT1

T2

T3

D

T…

D1 D2 D3

Term Partitioning

DocumentPartitioning

partitions

…

…

…

… … … … …

replicasbrokers

Typical Search Architecture

Managing Relational Data


Managing Relational Data In the “good old days”, organizations used relational

databases to manage big data Then along came Hadoop… Where does MapReduce fit in?

BTW, Hadoop is “hot” in

the SIGMOD community…

Relational Databases vs. MapReduce Relational databases:

Multipurpose: analysis and transactions; batch and interactive Data integrity via ACID transactions Lots of tools in software ecosystem (for ingesting, reporting, etc.) Supports SQL (and SQL integration, e.g., JDBC) Automatic SQL query optimization

MapReduce (Hadoop): Designed for large clusters, fault tolerant Data is accessed in “native format” Supports many query languages Programmers retain control over performance Open source

Source: O’Reilly Blog post by Joseph Hellerstein (11/19/2008)

Database Workloads OLTP (online transaction processing)

Typical applications: e-commerce, banking, airline reservations User facing: real-time, low latency, highly-concurrent Tasks: relatively small set of “standard” transactional queries Data access pattern: random reads, updates, writes (involving

relatively small amounts of data) OLAP (online analytical processing)

Typical applications: business intelligence, data mining Back-end processing: batch workloads, less concurrency Tasks: complex analytical queries, often ad hoc Data access pattern: table scans, large amounts of data involved

per query

One Database or Two? Downsides of co-existing OLTP and OLAP workloads

Poor memory management Conflicting data access patterns Variable latency

Solution: separate databases User-facing OLTP database for high-volume transactions Data warehouse for OLAP workloads How do we connect the two?

OLTP/OLAP Architecture

OLTP OLAPETL

(Extract, Transform, and Load)

OLTP/OLAP Integration OLTP database for user-facing transactions

Retain records of all activity Periodic ETL (e.g., nightly)

Extract-Transform-Load (ETL) Extract records from source Transform: clean data, check integrity, aggregate, etc. Load into OLAP database

OLAP database for data warehousing Business intelligence: reporting, ad hoc queries, data mining, etc. Feedback to improve OLTP services

Business Intelligence Premise: more data leads to better business decisions

Periodic reporting as well as ad hoc queries Analysts, not programmers (importance of tools and dashboards)

Examples: Slicing-and-dicing activity by different dimensions to better

understand the marketplace Analyzing log data to improve OLTP experience Analyzing log data to better optimize ad placement Analyzing purchasing trends for better supply-chain management Mining for correlations between otherwise unrelated activities

OLTP/OLAP Architecture: Hadoop?

OLTP OLAPETL


Hadoop here?

What about here?

OLTP/OLAP/Hadoop Architecture

OLTP OLAPETL


Hadoop

Why does this make sense?

ETL Bottleneck Reporting is often a nightly task:

ETL is often slow: why? What happens if processing 24 hours of data takes longer than 24

hours? Hadoop is perfect:

Most likely, you already have some data warehousing solution Ingest is limited by speed of HDFS Scales out with more nodes Massively parallel Ability to use any processing tool Much cheaper than parallel databases ETL is a batch process anyway!

Working Scenario Two tables:

User demographics (gender, age, income, etc.) User page visits (URL, time spent, etc.)

Analyses we might want to perform: Statistics on demographic characteristics Statistics on page visits Statistics on page visits by URL Statistics on page visits by demographic characteristic …

How to perform common relational operations in MapReduce… Except, don’t! (later)

Relational Algebra Primitives

Projection () Selection () Cartesian product () Set union () Set difference () Rename ()

Other operations Join ( )⋈ Group by… aggregation …

Projection

R1

R2

R3

R4

R5

R1

R2

R3

R4

R5

Projection in MapReduce Easy!

Map over tuples, emit new tuples with appropriate attributes No reducers, unless for regrouping or resorting tuples Alternatively: perform in reducer, after some other processing

Basically limited by HDFS streaming speeds Speed of encoding/decoding tuples becomes important Relational databases take advantage of compression Semistructured data? No problem!

Selection

R1

R2

R3

R4

R5

R1

R3

Selection in MapReduce Easy!

Map over tuples, emit only tuples that meet criteria No reducers, unless for regrouping or resorting tuples Alternatively: perform in reducer, after some other processing

Basically limited by HDFS streaming speeds Speed of encoding/decoding tuples becomes important Relational databases take advantage of compression Semistructured data? No problem!

Group by… Aggregation Example: What is the average time spent per URL? In SQL:

SELECT url, AVG(time) FROM visits GROUP BY url In MapReduce:

Map over tuples, emit time, keyed by url Framework automatically groups values by keys Compute average in reducer Optimize with combiners

Relational JoinsR1

R2

R3

R4

S1

S2

S3

S4

R1 S2

R2 S4

R3 S1

R4 S3

Types of Relationships

One-to-OneOne-to-ManyMany-to-Many

Join Algorithms in MapReduce Reduce-side join Map-side join In-memory join

Striped variant Memcached variant

Reduce-side Join Basic idea: group by join key

Map over both sets of tuples Emit tuple as value with join key as the intermediate key Execution framework brings together tuples sharing the same key Perform actual join in reducer Similar to a “sort-merge join” in database terminology

Two variants 1-to-1 joins 1-to-many and many-to-many joins

Reduce-side Join: 1-to-1

R1

R4

S2

S3

R1

R4

S2

S3

keys valuesMap

R1

R4

S2

S3

keys values

Reduce

Note: no guarantee if R is going to come first or S

Reduce-side Join: 1-to-many

R1

S2

S3

R1

S2

S3

S9

keys valuesMap

R1 S2

keys values

Reduce

S9

S3 …


Reduce-side Join: V-to-K Conversion

R1

keys values

In reducer…

S2

S3

S9

R4

S3

S7

New key encountered: hold in memory

Cross with records from other set

New key encountered: hold in memory


Reduce-side Join: many-to-many

R1

keys values

In reducer…

S2

S3

S9

Hold in memory


R5

R8


Map-side Join: Basic IdeaAssume two datasets are sorted by the join key:

R1

R2

R3

R4

S1

S2

S3

S4

A sequential scan through both datasets to join(called a “merge join” in database terminology)

Map-side Join: Parallel Scans If datasets are sorted by join key, join can be

accomplished by a scan over both datasets How can we accomplish this in parallel?

Partition and sort both datasets in the same manner In MapReduce:

Map over one dataset, read from other corresponding partition No reducers necessary (unless to repartition or resort)

Consistently partitioned datasets: realistic to expect?

In-Memory Join Basic idea: load one dataset into memory, stream over

other dataset Works if R << S and R fits into memory Called a “hash join” in database terminology

MapReduce implementation Distribute R to all nodes Map over S, each mapper loads R in memory, hashed by join key For every tuple in S, look up join key in R No reducers, unless for regrouping or resorting tuples

In-Memory Join: Variants Striped variant:

R too big to fit into memory? Divide R into R1, R2, R3, … s.t. each Rn fits into memory Perform in-memory join: n, Rn S⋈ Take the union of all join results

Memcached join: Load R into memcached Replace in-memory hash lookup with memcached lookup

Which join to use? In-memory join > map-side join > reduce-side join

Why? Limitations of each?

In-memory join: memory Map-side join: sort order and partitioning Reduce-side join: general purpose

Key Features in Databases Common optimizations in relational databases

Reducing the amount of data to read Reducing the amount of tuples to decode Data placement Query planning and cost estimation

Same ideas can be applied to MapReduce For example, column stores in Google Dremel A few commercialized products Many research prototypes

One size does not fit all… Databases when:

You know what the question is: query optimizers work well Well-specified schema, clean data

MapReduce when: You don’t necessarily know what the question is: go brute force Exploratory data analysis Semi-structured, noisy, diverse data ETL is the insight-generation process

Graph Algorithms


What’s a graph? G = (V,E), where

V represents the set of vertices (nodes) E represents the set of edges (links) Both vertices and edges may contain additional information

Different types of graphs: Directed vs. undirected edges Presence or absence of cycles

Graphs are everywhere: Hyperlink structure of the Web Physical structure of computers on the Internet Interstate highway system Social networks

Source: Wikipedia (Königsberg)

Some Graph Problems Finding shortest paths

Routing Internet traffic and UPS trucks Finding minimum spanning trees

Telco laying down fiber Finding Max Flow

Airline scheduling Identify “special” nodes and communities

Breaking up terrorist cells, spread of avian flu Bipartite matching

Monster.com, Match.com And of course... PageRank

Graphs and MapReduce Graph algorithms typically involve:

Performing computations at each node: based on node features, edge features, and local link structure

Propagating computations: “traversing” the graph Key questions:

How do you represent graph data in MapReduce? How do you traverse a graph in MapReduce?

Representing Graphs G = (V, E) Two common representations

Adjacency matrix Adjacency list

Adjacency MatricesRepresent a graph as an n x n square matrix M

n = |V| Mij = 1 means a link from node i to j

1 2 3 41 0 1 0 12 1 0 1 13 1 0 0 04 1 0 1 0

1

2

3

4

Adjacency Matrices: Critique Advantages:

Amenable to mathematical manipulation Iteration over rows and columns corresponds to computations on

outlinks and inlinks Disadvantages:

Lots of zeros for sparse matrices Lots of wasted space

Adjacency ListsTake adjacency matrices… and throw away all the zeros

1: 2, 42: 1, 3, 43: 14: 1, 3

1 2 3 41 0 1 0 12 1 0 1 13 1 0 0 04 1 0 1 0

Adjacency Lists: Critique Advantages:

Much more compact representation Easy to compute over outlinks

Disadvantages: Much more difficult to compute over inlinks

Single Source Shortest Path Problem: find shortest path from a source node to one or

more target nodes Shortest might also mean lowest weight or cost

First, a refresher: Dijkstra’s Algorithm

Dijkstra’s Algorithm Example

0

10

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2 3

2

1

9

7

4 6

Example from CLR


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10

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Example from CLR

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2 3

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1

9

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4 6


0

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5

14

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Example from CLR

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1

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Example from CLR

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Example from CLR

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Example from CLR

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Single Source Shortest Path Problem: find shortest path from a source node to one or

more target nodes Shortest might also mean lowest weight or cost

Single processor machine: Dijkstra’s Algorithm MapReduce: parallel Breadth-First Search (BFS)

Finding the Shortest Path Consider simple case of equal edge weights Solution to the problem can be defined inductively Here’s the intuition:

Define: b is reachable from a if b is on adjacency list of a DISTANCETO(s) = 0 For all nodes p reachable from s,

DISTANCETO(p) = 1 For all nodes n reachable from some other set of nodes M,

DISTANCETO(n) = 1 + min(DISTANCETO(m), m M)

s

m3

m2

m1

n

…

…

…

d1

d2

d3

Source: Wikipedia (Wave)

Visualizing Parallel BFS

n0

n3n2

n1

n7

n6

n5

n4

n9

n8

From Intuition to Algorithm Data representation:

Key: node n Value: d (distance from start), adjacency list (list of nodes

reachable from n) Initialization: for all nodes except for start node, d =

Mapper: m adjacency list: emit (m, d + 1)

Sort/Shuffle Groups distances by reachable nodes

Reducer: Selects minimum distance path for each reachable node Additional bookkeeping needed to keep track of actual path

Multiple Iterations Needed Each MapReduce iteration advances the “known frontier”

by one hop Subsequent iterations include more and more reachable nodes as

frontier expands Multiple iterations are needed to explore entire graph

Preserving graph structure: Problem: Where did the adjacency list go? Solution: mapper emits (n, adjacency list) as well

BFS Pseudo-Code

Stopping Criterion How many iterations are needed in parallel BFS (equal

edge weight case)? When a node is first “discovered”, we’re guaranteed to

have found the shortest path

Comparison to Dijkstra Dijkstra’s algorithm is more efficient

At any step it only pursues edges from the minimum-cost path inside the frontier

MapReduce explores all paths in parallel Lots of “waste” Useful work is only done at the “frontier”

Why can’t we do better using MapReduce?

Weighted Edges Now add positive weights to the edges Simple change: adjacency list now includes a weight w for

each edge In mapper, emit (m, d + wp) instead of (m, d + 1) for each node m

That’s it?

Stopping Criterion How many iterations are needed in parallel BFS (positive

edge weight case)? When a node is first “discovered”, we’re guaranteed to

have found the shortest path

Not true!

Additional Complexities

s

pq

r

search frontier

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n1

n2

n3

n4

n5

n6 n7n8

n9

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Stopping Criterion How many iterations are needed in parallel BFS (positive

edge weight case)? Practicalities of implementation in MapReduce

Graphs and MapReduce Graph algorithms typically involve:

Performing computations at each node: based on node features, edge features, and local link structure

Propagating computations: “traversing” the graph Generic recipe:

Represent graphs as adjacency lists Perform local computations in mapper Pass along partial results via outlinks, keyed by destination node Perform aggregation in reducer on inlinks to a node Iterate until convergence: controlled by external “driver” Don’t forget to pass the graph structure between iterations

Random Walks Over the Web Random surfer model:

User starts at a random Web page User randomly clicks on links, surfing from page to page

PageRank Characterizes the amount of time spent on any given page Mathematically, a probability distribution over pages

PageRank captures notions of page importance Correspondence to human intuition? One of thousands of features used in web search Note: query-independent

Given page x with inlinks t1…tn, where C(t) is the out-degree of t is probability of random jump N is the total number of nodes in the graph

PageRank: Defined

n

i i

i

tCtPR

NxPR

1 )()()1(1)(

X

t1

t2

tn

…

Computing PageRank Properties of PageRank

Can be computed iteratively Effects at each iteration are local

Sketch of algorithm: Start with seed PRi values Each page distributes PRi “credit” to all pages it links to Each target page adds up “credit” from multiple in-bound links to

compute PRi+1

Iterate until values converge

Simplified PageRank First, tackle the simple case:

No random jump factor No dangling links

Then, factor in these complexities… Why do we need the random jump? Where do dangling links come from?

Sample PageRank Iteration (1)

n1 (0.2)

n4 (0.2)

n3 (0.2)n5 (0.2)

n2 (0.2)

0.1

0.1

0.2 0.2

0.1 0.1

0.066 0.0660.066

n1 (0.066)

n4 (0.3)

n3 (0.166)n5 (0.3)

n2 (0.166)Iteration 1

Sample PageRank Iteration (2)

n1 (0.066)

n4 (0.3)

n3 (0.166)n5 (0.3)

n2 (0.166)

0.033

0.033

0.3 0.166

0.083 0.083

0.1 0.10.1

n1 (0.1)

n4 (0.2)

n3 (0.183)n5 (0.383)

n2 (0.133)Iteration 2

PageRank in MapReduce

n5 [n1, n2, n3]n1 [n2, n4] n2 [n3, n5] n3 [n4] n4 [n5]

n2 n4 n3 n5 n1 n2 n3n4 n5

n2 n4n3 n5n1 n2 n3 n4 n5

n5 [n1, n2, n3]n1 [n2, n4] n2 [n3, n5] n3 [n4] n4 [n5]

Map

Reduce

PageRank Pseudo-Code

Complete PageRank Two additional complexities

What is the proper treatment of dangling nodes? How do we factor in the random jump factor?

Solution: Second pass to redistribute “missing PageRank mass” and

account for random jumps

p is PageRank value from before, p' is updated PageRank value |G| is the number of nodes in the graph m is the missing PageRank mass

p

Gm

Gp )1(1'

PageRank Convergence Alternative convergence criteria

Iterate until PageRank values don’t change Iterate until PageRank rankings don’t change Fixed number of iterations

Convergence for web graphs?

Beyond PageRank Link structure is important for web search

PageRank is one of many link-based features: HITS, SALSA, etc. One of many thousands of features used in ranking…

Adversarial nature of web search Link spamming Spider traps Keyword stuffing …

Efficient Graph Algorithms: Tricks In-mapper combining: efficient local aggregation Smarter partitioning: create more opportunities for local

aggregation Schimmy: avoid shuffling the graph

Jimmy Lin and Michael Schatz. Design Patterns for Efficient Graph Algorithms in MapReduce. Proceedings of the Eighth Workshop on Mining and Learning with Graphs Workshop (MLG-2010), pages 78-85, July 2010, Washington, D.C.

In-Mapper Combining Use combiners

Perform local aggregation on map output Downside: intermediate data is still materialized

Better: in-mapper combining Preserve state across multiple map calls, aggregate messages in

buffer, emit buffer contents at end Downside: requires memory management

configure

map

close

buffer

Better Partitioning Default: hash partitioning

Randomly assign nodes to partitions Observation: many graphs exhibit local structure

E.g., communities in social networks Better partitioning creates more opportunities for local aggregation

Unfortunately, partitioning is hard! Sometimes, chick-and-egg… But cheap heuristics sometimes available For webgraphs: range partition on domain-sorted URLs

Schimmy Design Pattern Basic implementation contains two dataflows:

Messages (actual computations) Graph structure (“bookkeeping”)

Schimmy: separate the two data flows, shuffle only the messages Basic idea: merge join between graph structure and messages

S T

both relations sorted by join key

S1 T1 S2 T2 S3 T3

both relations consistently partitioned and sorted by join key

S1 T1

Do the Schimmy! Schimmy = reduce side parallel merge join between graph

structure and messages Consistent partitioning between input and intermediate data Mappers emit only messages (actual computation) Reducers read graph structure directly from HDFS

S2 T2 S3 T3

ReducerReducerReducer

intermediate data(messages)



from HDFS(graph structure)



Experiments Cluster setup:

10 workers, each 2 cores (3.2 GHz Xeon), 4GB RAM, 367 GB disk Hadoop 0.20.0 on RHELS 5.3

Dataset: First English segment of ClueWeb09 collection 50.2m web pages (1.53 TB uncompressed, 247 GB compressed) Extracted webgraph: 1.4 billion links, 7.0 GB Dataset arranged in crawl order

Setup: Measured per-iteration running time (5 iterations) 100 partitions

Results

“Best Practices”

Results

+18%1.4b

674m

Results

+18%

-15%

1.4b

674m

Results

+18%

-15%

-60%

1.4b

674m

86m

Results

+18%

-15%

-60%-69%

1.4b

674m

86m

Aside: How to do this better… MapReduce is a poor abstraction for graphs

No separation of computation from graph structure Poor locality: unnecessary data movement

Bulk synchronous parallel (BSP) as a better model: Google’s Pregel, open source Giraph clone

Bulk Synchronous Parallel (BSP) Computation is modeled as series of supersteps

All data held in memory At each iteration:

Each vertex invokes a function in parallel Can modify vertex state and edge state Can read messages sent in previous superstep Can send messages (to arbitrary vertices) to be read in next

superstep Synchronization barrier between each superstep

Interesting (open?) question: how many hammers and how many nails?

Questions?

Large-Scale Data Processing with MapReduce

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