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

Apr 26 th, 2006 Christian Frank 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

Apr 26 th, 2006 Christian Frank 3 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

Apr 26 th, 2006 Christian Frank 4 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

Apr 26 th, 2006 Christian Frank 5  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 on off ON :: { temp-sensor == true && battery >= threshold && count(2 meters) { role == ON } == 0 } OFF :: else  count(scope) { pred }:  Counts nodes matching pred within scope

Apr 26 th, 2006 Christian Frank 6 RA Algorithm Property Directory App. Distributed Algorithm Role Specifications Elements of a Role-Assignment System Node Properties Network Role Assignment Problem RA Algorithm Role Assignment battery = 80% pos = (12, 3) role = ON …

Apr 26 th, 2006 Christian Frank 7  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? on off

Apr 26 th, 2006 Christian Frank 8 Role Specifications Verification through Integer Program Node Properties Network Role 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)

Apr 26 th, 2006 Christian Frank 9 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 1 if node i is assigned role r 0 otherwise M high number, annuls constraint

Apr 26 th, 2006 Christian Frank 10 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

Apr 26 th, 2006 Christian Frank 11 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

Apr 26 th, 2006 Christian Frank 12  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

Apr 26 th, 2006 Christian Frank 13  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