High-Concurrency Locking in R-Trees

High-Concurrency Locking inR-Trees

Presented by: Robertas Kerpys

Marcel Kornacker Universität Hamburg

Douglas Banks University of

California at Berkeley

VLDB 1995

November 11, 2010

Database Specialization Course 2

Motivation

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p1

p16

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p5p6

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R2

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p1 p2 p3 p4 p5 p13 p6 p7p11 p12p8 p9 p10

R5 R6 R7

R3

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R5R6

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R3 R4

R1 R2

p16

Query


Motivation

November 11, 2010

p1

p16

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p1 p2 p3 p4 p5 p13 p6 p7p11 p12p8 p9 p10

R5 R6 R7

R3

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R1 R2

p16

Query


Motivation

November 11, 2010

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p1 p2 p5 p16p3 p4 p13 p6 p7p11 p12p8 p9 p10

R5 R6 R7

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R3 R4 R8

R1 R2 Query

R8


Motivation

• Concurrency requires special handling of the index structure to ensure consistency

• Many of the methods which offers concurrent tree traversal employ top-down lock-coupling

• Main goal is to enable queries and updates execute concurrently while ensuring the correctness of the results

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Overview

• Motivation• B-link tree• R-link tree• Algorithms (Search, Insert, Delete)• Empirical study• Conclusion• Critique

November 11, 2010


Blink - tree

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Obstacles

• The main difficulty is that R-tree does not have a linear ordering

• Keys cannot conclusively tell us when a node has split

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p1

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R2R1

p1 p2 p3 p4 p5 p13 p6 p7p11 p12p8 p9 p10

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R3R5

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R1 R2


How to adapt links on an R-tree?

• System of sequence numbers is introduced to determine when and how to traverse sibling links

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Structure of an R-link tree

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5 6 4 2 1c1 c2 c3 c4 c5

5x

2y

4w

1z

p1 p2


Search

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5 6 4 2 1c1 c2 c3 c4 c5

5x

2y

4w

1z

p1 p2

zwyx

c5c2 c3

Qualifyingentries:

Stack


Insertioninsert(Rect r):

stack = findLeaf(root, r, root-lsn)leaf = pop(stack)insert r on leafif leaf was split

extendParent(leaf, leaf.MBR, leaf.LSN, right_sibling, right_sibling.MBR, right_sibling.LSN,

stack)else

if bounding-rect of leaf changed updateParent(leaf, leaf.MBR, stack)

elsew-unlock(leaf)

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Insertion. Find Leaf

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p1 p2 p3 p4 p5 p13 p6 p7p11 p12p8 p9 p10

R5 R6 R7R3 R4

R1 R2findLeaf(root, r, root-lsn)

Stack:

N

N1 N2

N3 N4 N5 N6 N7

N

N1

N4

- shared lock - exclusive lock


Insertion. Extend Parent

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p1 p2 p3 p4 p13 p6 p7p11 p12p8 p9 p10

R5 R6 R7R3 R4

R1 R2extendParent

Stack:

N

N1 N2

N3 N4 N5 N6 N7

N N1

- shared lock - exclusive lock

p5 p16

R8

N8


Deletion

• A combination of the search and insert algorithms

• Nodes are removed as soon as they become empty

• In order to not employ the lock-coupling when descending the tree we have to take care of invalid pointers when removing nodes

• A tree-global generation counter (TGC) is introduced

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Deletion

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p13 p6 p7p11 p12p8 p9 p10

R5 R6 R7R3 R4

R1 R2N1 N2

N3 N4 N5 N6 N7p5 p16

R8

TGC

9

p2p1

10

p4p3

N = 9

N

N1 = 9N2 = 9N3 = 9

N4 = 9N5 = 9N6 = 9N7 = 9

N4 = 10


Overview

• Motivation• B-link tree• R-link tree• Algorithms (Search, Insert, Delete)• Empirical study• Conclusion• Critique

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Experimental Setup

• R-tree implementation employs a variation of Bayer-Schkolnick-style lock-coupling for concurrent insertions

• Three different workloads:– The low-contention workload consists of a varying number

of searchers and a single inserter– The moderate-contention workload of inserters only– The high-contention workload of an equal number of

searchers and inserters• The index was pre-loaded with 30600 2-dimensional

non-overlapping rectangles

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Empirical Evaluation

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Empirical Evaluation (cont.)

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Related Work

• Blink – tree “Efficient Locking for Concurrent Operations on B-trees” by Philip L. Lehman, S. Bing Yao– Applied on B-trees– All ideas are drawn from this paper

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Conclusion

• R-link trees look and work similar to B-link trees

• Holds only a few locks at one time• Descending an R-link tree to a leaf requires no

lock-coupling

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Critique. Advantages

• Recovery is addressed• R-link tree was implemented for commercial

database• Examples were good and where needed

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Critique. Disadvantages

• Workload is to small (30600 rectangles which does not even overlap)

• Authors review only papers for concurrency in B-trees

• They did not implemented everything they talked about

• The notation in pseudo-code is not introduced in the text thus it was not obvious right away e.g. r-lock

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Thank you!

November 11, 2010


Questions?Spørgsmål?Întrebare? Klausimai?

November 11, 2010

High-Concurrency Locking in R-Trees

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