Solving Generic Role Assignment Exactly

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Solving Generic Role Assignment Exactly

• Christian Frank and Kay Römer
• ETH Zurich, Switzerland

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Programming Abstractions for WSN

• Task at hand on a higher level
• Retrieve data from network (TinyDB)
• Assign different functions to network nodes (Role
  Assignment)

• Wireless Sensor Networks
• Small sensing devices, communicating wirelessly
• Allow unobtrusive monitoring of physical
  processes
• Programmed as a distributed system

read_sensor() send_msg() get_pos()
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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

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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

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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 temp-sensor true battery gt
threshold count(2 meters) role ON
0 OFF else

• x retrieve(scope) pred
• store nodes matching pred in property x

• count(scope) pred
• Counts nodes matching pred within scope

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Elements of a Role-Assignment System
Role Specifications
Node Properties
Network
Role Assignment Problem
RA Algorithm
battery 80 pos (12, 3) role ON
Role Assignment
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Distributed Algorithm

• 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

• Does solution exist?
• How good is the solution?

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Verification through Integer Program
Role Specifications
Node Properties
Network
Role Assignment Problem
RA Algorithm

• Detect infeasible specifications
• Optimize number of nodes with a certain role(s)

Role Assignment
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Example Integer Program
ON count(scope) role ON lt 0
OFF else

• 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

M high number, annuls constraint
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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 gt
threshold count(2 meters) role ON
0 OFF else
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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

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Results Optimality

• IP can be used to compute gap between
  distributed and optimal configuration
• Generated IPs computable in reasonable time for
  many nodes

ON nodes with Coverage Example
Distributed
IP
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Summary

• 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

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Solving Generic Role Assignment Exactly

• Christian Frank and Kay Römer
• ETH Zurich, Switzerland