Apr 26th, 2006 Solving Generic Role Assignment Exactly Christian Frank and Kay Römer ETH Zurich,...

Apr 26th, 2006

Solving Generic Role Assignment Exactly

Christian Frank and Kay Römer

ETH Zurich, Switzerland

Apr 26th, 2006 Christian Frank <[email protected]> 2

Programming Abstractions for WSN

Task at hand on a higher level: Retrieve data from network

(TinyDB) Assign different functions to

network nodes (Role Assignment)

read_sensor()send_msg() get_pos()

Wireless Sensor Networks Small sensing devices,

communicating wirelessly Allow unobtrusive monitoring of

physical processes Programmed as a distributed

system


Role Assignment Problems

Coverage Roles ON, OFF ON nodes cover every geographic spot

Clustering Roles: Clusterhead, Gateway, Slave Connected Subgraph

Data Aggregation Roles: Data Source, Aggregator, Forwarder

Many variations and combinations of the above


Role Assignment Abstraction

Programmer defines a list of roles Functions that a node may perform in the network

Annotated with conditions for assigning each role, based on: Local node properties (available sensors, processing

power, battery, position…) Properties of nodes in network neighborhood


x == retrieve(scope) { pred } : store nodes matching pred in property x

Example Specification: Coverage Network consists of more

nodes than needed

Only some nodes need to have sensors ON

Others may save power and sleep with sensors OFF

Conditions of ON role: Temperature sensor Battery above threshold No other ON node in sensing

range

onoff

ON :: {temp-sensor == true &&battery >= threshold &&count(2 meters) {

role == ON} == 0

}OFF :: else

count(scope) { pred }: Counts nodes matching pred within scope


RA Algorithm

Property Directory

App.

Distributed Algorithm

Role Specifications

Elements of a Role-Assignment SystemNode PropertiesNetworkRole

Assignment Problem

RA Algorithm

Role Assignment

battery = 80%pos = (12, 3)role = ON …


Distributed algorithm repeats three basic steps: Send properties to neighbors Wait random interval, receive properties Decide role

Distributed fixpoint iteration Notifies applications on stable role Details in “Algorithms for Generic Role

Assignment…” In Proc. of Sensys 2005

Distributed Algorithm

Does solution exist?How good is the solution?

onoff


Role Specifications

Verification through Integer ProgramNode PropertiesNetworkRole

Assignment Problem

RA Algorithm

Role Assignment

IP Converter

Integer Program

CPLEX Solver

Centralized Algorithm Detect infeasible

specifications Optimize number

of nodes with a certain role(s)


Example Integer Program

Binary result variables For each node i and role r

Constraints (for each node i ): Only one role should be

assigned to a node i Role ON is assigned iff

count operator is true “ “: If role ON,

count must be true “ “ similar

ON :: {count(scope) {

role == ON } <= 0 }

OFF :: else

( ,ON) ( ,OFF) 1x i x i

scope

( , ) 0j

x j ON

( ,ON) 1x i

scope

( , ) 0 (1 ( , ))j

x j ON M x i ON

( , )x i r 1 if node i is assigned role r0 otherwise

M high number, annuls constraint


Additional Variables and Constraints Variables

Output variables indicating computed role

Auxiliary variables at each node- For each atomic predicate - For each and / or- For each role condition (opposed

to assignment)

Constraints formulating And / or Assign first matching role, if

more than one condition matches

Retrieve operators (paper)

ON :: { temp-sensor == true && battery >= threshold && count(2 meters) {

role == ON } == 0 }OFF :: else

1y

2y

3y

ON 1 2 3c y y y

ONc

OFFc

OFF OFF ONx c c

ON 1 2 33c y y y


Results: Feasibility

Some specifications are infeasible, toy example: Condition for Red: At least 1 Green neighbor Condition for Green: No Red neighbor Grey: Else

Infeasibility is not always apparent in the specification Distributed algorithm does not find solution

IP can be used to detect infeasibility Compute feasible topology


IP can be used to compute gap between “distributed” and “optimal” configuration

Generated IPs computable in reasonable time for many nodes

Results: Optimality

IP

Distributed

ON nodes with Coverage Example


IP-based role assignment algorithm Compute feasibility (or feasible topology) Optimize number of nodes with a certain role(s)

Integrated development tool Simulator of distributed algorithms Integer-program based verifier Visualization

Summary

Apr 26th, 2006

Solving Generic Role Assignment Exactly

Christian Frank and Kay Römer

ETH Zurich, Switzerland

Apr 26th, 2006 Solving Generic Role Assignment Exactly Christian Frank and Kay Römer ETH Zurich,...

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