Agent-friendly aggregation 1 On agent-friendly aggregation in networks ATSN 2008 (at AAMAS 2008) Christian Sommer and Shinichi Honiden National Institute of Informatics, The University of Tokyo Tokyo, Japan

Agent-friendly aggregation 2 Agenda Sensor networks Aggregation Agent aggregation specifics Problem model: aggregation graph Computing a tour

Agent-friendly aggregation 3 Sensor networks Sense/measure the environment –Temperature –Sound –Vibration –Pressure –Motion –…

Agent-friendly aggregation 4 Sensor networks Base station

Agent-friendly aggregation 5 Wireless sensor networks Base station

Agent-friendly aggregation 6 Example: Sun SPOT Sensors Processing – 180 MHz 32 bit ARM920T core - 512K RAM - 4M Flash –2.4 GHz IEEE radio with integrated antenna Sensor Board Battery –3.6V rechargeable 750 mAh lithium-ion battery –30 uA deep sleep mode

Agent-friendly aggregation 7 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

Agent-friendly aggregation 8 Aggregation tree Base station

Agent-friendly aggregation 9 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.

Agent-friendly aggregation 10 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

Agent-friendly aggregation 11 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

Agent-friendly aggregation 12 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

Agent-friendly aggregation 13 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!

Agent-friendly aggregation 14 Aggregation tree Base station

Agent-friendly aggregation 15 Problem modelling Sensor network as undirected graph Base station

Agent-friendly aggregation 16 Problem modelling Sensor network as undirected graph Base station

Agent-friendly aggregation 17 Problem modelling Sensor network as undirected graph

Agent-friendly aggregation 18 Assumption Graph is known (to base station) (i.e. sensors and their adjacency is known) … and does not change, static

Agent-friendly aggregation 19 Hamiltonian cycle Given a graph G=(V,E) Find a cycle visiting all nodes Hard problem

Agent-friendly aggregation 20 Travelling Salesman (TSP) Given a weighted graph G=(V,E) Find shortest tour visiting all nodes Compare all Hamiltonian cycles Hard problem

Agent-friendly aggregation 21 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

Agent-friendly aggregation 22 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)

Agent-friendly aggregation 23 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 24 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 25 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

Agent-friendly aggregation 26 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 27 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 28 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

Agent-friendly aggregation 29 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 30 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

Agent-friendly aggregation 31 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 32 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

Agent-friendly aggregation 33 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 34 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

Agent-friendly aggregation 35 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit) 1)Remove trees, 2-core remains 2)While no cycle is found, backtrack through different rotations (permutations) 1)Take a path from the list of partial paths 2)Try to extend it at either side with an unvisited node If 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

Agent-friendly aggregation 36 Hamiltonian cycle for unit disk graphs (Bollobas et al., Petit)

Agent-friendly aggregation 37 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)

Agent-friendly aggregation 38 Thank you