Agent-friendly aggregation 1

On agent-friendly aggregation in networks

ATSN 2008 (at AAMAS 2008)

Christian Sommer and Shinichi HonidenNational Institute of Informatics,

The University of Tokyo

Tokyo, Japan

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Agenda

• Sensor networks

• Aggregation

• Agent aggregation specifics

• Problem model: aggregation graph

• Computing a tour

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Sensor networks

• Sense/measure the environment– Temperature– Sound– Vibration– Pressure– Motion– …

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Sensor networks

Base station

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Wireless sensor networks

Base station

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Example: Sun SPOT Sensors

• Processing– 180 MHz 32 bit ARM920T core - 512K RAM - 4M Flash

– 2.4 GHz IEEE 802.15.4 radio with integrated antenna

• Sensor Board• Battery

– 3.6V rechargeable 750 mAh lithium-ion battery

– 30 uA deep sleep mode

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Data aggregation

• Severe resource limitations (battery, sending power)

• Often high redundancy of sensor measurements (time and space)

• Aggregate data before sending it to the base station (e.g., AVG, SUM, MIN,…)

• Aggregation tree

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Aggregation tree

Base station

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Aggregation using a mobile (software) agent

• Code is sent through the sensor network…

• … runs on (all/some) network nodes …– collects and aggregates data

• … and returns to the base station.

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Pros and cons of the agent approach

Advantages:• ability to use code /

aggregation function, which is– Application-specific– Dynamic– Non-local

Problems:• Time• Code size• Security• Aggregation tour

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Pros and cons of the agent approach

Advantages:• ability to use code /

aggregation function, which is– Application-specific– Dynamic– Non-local

Problems:• Time• Code size• Security• Aggregation tour

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Pros and cons of the agent approach

Advantages:• ability to use code /

aggregation function, which is– Application-specific– Dynamic– Non-local

Problems:• Time• Code size• Security• Aggregation tour

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What route to take?

• Visit all nodes

• Energy-efficiency– Avoid visiting nodes/edges several times

(possible exception: base station)• Possibly not a tree-like structure!

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Aggregation tree

Base station

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Problem modelling

• Sensor network as undirected graph

Base station

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Problem modelling

• Sensor network as undirected graph

Base station

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Problem modelling

• Sensor network as undirected graph

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Assumption

• Graph is known (to base station)

• (i.e. sensors and their adjacency is known)

• … and does not change, static

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Hamiltonian cycle

• Given a graph G=(V,E)

• Find a cycle visiting all nodes

• Hard problem

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Travelling Salesman (TSP)

• Given a weighted graph G=(V,E)

• Find shortest tour visiting all nodes

• Compare all Hamiltonian cycles

• Hard problem

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Hard problems?

• Hard in the worst case• But: there is hope for some graphs;

problems are solvable on average for these instances

• Unit disk model: n nodes are distributed uniformly at random in the unit disk, nodes within distance r (trans-mission radius) can communicate

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Assumption

• Apart from base station, all sensors can send and receive within the same distance, not possible to adapt signal strength (due to unit disk model)

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

1) Remove trees, 2-core remains2) While no cycle is found, backtrack through

different rotations (permutations)1) Take a path from the list of partial paths2) Try to extend it at either side with an unvisited

nodeIf impossible,

1) If cyclic, search for a node with a yet unvisited neighbor (exists due to connectivity)

2) Else, for endpoints, check for another adjacent node on the path and rotate

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Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

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Conclusion

• If agent-based aggregation is benefitial in a sensor network, it can be done quite efficiently.

• (the algorithm of Bollobas et al. quickly computes an energy-efficient tour (a Hamiltonian cycle) in a unit disk graph)

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Thank you