Wireless Distributed Sensor Tracking: Computation and Communication Bart Selman, Carla Gomes, Scott Kirkpatrick, Ramon Bejar, Bhaskar Krishnamachari, Johannes Schneider Intelligent Information Systems Institute, Cornell University & Hebrew University Autonomous Negotiating Teams Principal Investigators' Meeting, Oct. 19, 2001

Outline Overview of our approach Ants - Challenge Problem (Sensor Domain) Graph Models Results on average case complexity Distributed CSP model Phase Transitions --- 3D view (communication vs. complexity vs. overall performance) Conclusions and Future Work

Overview of Approach Overall theme --- exploit impact of structure on computational complexity Identification of domain structural features  tractable vs. intractable subclasses  phase transition phenomena  backbone  balancedness  … Goal:  Use findings in both the design and operation of distributed platform  Principled controlled hardness aware systems

ANTs Challenge Problem Multiple doppler radar sensors track moving targets Energy limited sensors Communication constraints Distributed environment Dynamic problem IISI, Cornell University

Domain Models Start with a simple graph model Successively refine the model in stages to approximate the real situation: Static weakly-constrained model Static constraint satisfaction model with communication constraints Static distributed constraint satisfaction model Dynamic distributed constraint satisfaction model Goal: Identify and isolate the sources of combinatorial complexity IISI, Cornell University

Initial Assumptions Each sensor can only track one target at a time 3 sensors are required to track a target IISI, Cornell University

Initial Graph Model Bipartite graph G = (S U T, E) S is the set of sensor nodes, T the set of target nodes, E the edges indicating which targets are visible to a given sensor Decision Problem: Can each target be tracked by three sensors? IISI, Cornell University

Initial Graph Model IISI, Cornell University Target visibility Graph Representation Sensor nodes Target nodes

Initial Graph Model IISI, Cornell University The initial model presented is a bipartite graph, and this problem can be solved using a maximum flow algorithm in polynomial time Results incorporated into framework developed by Milind Tambe’s group at ISI, USC Joint work in progress Sensor nodes Target nodes

Sensor Communication Constraints IISI, Cornell University initial model + communication edgesinitial model+ communication edges Possible solution In the graph model, we now have additional edges between sensor nodes

IISI, Cornell University Constrained Graph Model sensors targets communication links possible solution

Complexity and Phase Transition Phenomena

Worst-Case Complexity Decision Problem: Can each target be tracked by three sensors which can communicate together ? We have shown that this constraint satisfaction problem (CSP) is NP- complete, by reduction from the problem of partitioning a graph into isomorphic subgraphs IISI, Cornell University

What about average- case complexity?

Description of Experiments IISI, Cornell University Start with square area with unit sidesPlace sensors and targets randomly in areasensor target Create communication graph based on range Csensor target C sensor target C sensor target C Create visibility graph based on radar range R sensor target R sensor target RR sensor target R Combine the communication and visibility graphssensor target

Description of Experiments IISI, Cornell University Determine if all targets can be tracked by three communicating sensorssensor target

Limit cases

Phase Transition w.r.t. Communication Range: IISI, Cornell University Experiments with a configuration of 9 sensors and 3 targets such that there is a communication channel between two sensors with probability p Probability( all targets tracked ) Communication edge probability p Insights into the design and operation of sensor networks w.r.t. communication range Special case: all targets are visible to all sensors

Phase Transition w.r.t. Radar Detection Range IISI, Cornell University Experiments with a configuration of 9 sensors and 3 targets such that each sensor is able to detect targets within a range R Probability( all targets tracked ) Normalized Radar Range R Insights into the design and operation of sensor networks w.r.t. radar detection range Special case: all nodes can communicate

The full picture Communication vs. Radar Range vs. Performance

Radar range R: from 0 (no target is covered) to 1 (all targets covered) Comm. range C: from 0 (no sensors communicates) to 1 (all sensors comm.) IISI, Cornell University 5 targets, 15 sensors5 targets, 17 sensors Probability of tracking all targets

Distributed Computational Model In a Distributed Constraint Satisfaction Problem (DCSP), variables and constraints are distributed among multiple agents. It consists of: A set of agents 1, 2, … n A set of CSPs P 1, P 2, … P n, one for each agent There are intra-agent constraints and inter-agent constraints IISI, Cornell University

DCSP Models We can represent the sensor tracking problem as a DCSP using dual representations: One with each sensor as a distinct agent One with a distinct tracker agent for each target IISI, Cornell University

DCSP Models With the DCSP models, we study both per-node computational costs as well as inter-node communication costs DCSP algorithms: DIBT (Hamadi et al.) and ABT (Yokoo et al.) IISI, Cornell University

Target Tracker Agents Intra-agent constraints : Each target must be tracked by 3 communicating sensors to which it is visible Inter-agent constraints: No common sensors between targets 11xx10xxx xx1xxx1x1 t1 t2 xxx10xx11t3 s1s2s3s4s5s6s7s8s9 IISI, Cornell University

Sensor Agents Intra-agent constraints : Sensor must track at most 1 visible target Inter-agent constraints: 3 communicating sensors should track each target xx01 s1 s2 s4 t1t2t3t4 s3 xxx1 1x00 xxx1 Inter-agent constraints Inter-agent constraints => All sensors seeing a target must know which sensors are tracking the target IISI, Cornell University

Comparison of the two models ModelSensor-centeredTarget-centered Agents Vars for intra constraints Vars for inter constraints Intra-agent constraints Inter-agent constraints Sensors Targets Only one target 3 comm. sensors Targets Sensors -- 3 comm. sensors Only one target Sensor-centered Sensor-centered: To check the inter-agent constraints, sensors must maintain one variable for every target they can track, that indicates which 3 sensors are tracking it Target-centered: Target-centered: Does not need additional variables for the inter-agent constraints IISI, Cornell University

Computational Complexity Computational Complexity: total computation cost for all agents Communication Complexity Communication Complexity: total number of messages sent by all agents Communication range / Sensor (radar) range provides 3rd dimension. These measures can vary for the same problem when using different DCSP models IISI, Cornell University Communication vs. Radar Range vs. Computation

Average Complexity (target-centered) 5 targets and 17 sensors IISI, Cornell University X 10 4 Mean computational costProbability of Tracking

Average Complexity (target-centered) 5 targets and 17 sensors IISI, Cornell University 1000 Probability of TrackingMean communication cost

Implicit versus Explicit Constraints Explicit constraint: no two targets can be tracked by same sensor (e.g. t2, t3 cannot share s4 and t1, t3 cannot share s9) Implicit constraint: due to a chain of explicit constraints: (e.g. implicit constraint between s4 for t2 and s9 for t1 ) 11xx10xxx xx1xxx1x1 t1 t2 xxx10xx11t3 s1s2s3s4s5s6s7s8s9 Agent ordering can make a difference ! IISI, Cornell University

Communication Cost for Implicit Constraints Explicit constraints can be resolved by direct communication between agents Resolving Implicit constraints may require long communication paths through multiple agents  scalability problems 11xx10xxx xx1xxx1x1 t1 t2 xxx10xx11t3 s1s2s3s4s5s6s7s8s9

Future Work

Structure Further study structural issues as they occur in the Sensor domain e.g.: effect of balancing backbone (insights into critical resources) refinement of phase transition notions considering additional parameters (concepts introduced in previous PI meeting) IISI, Cornell University

Dynamic DCSP Model Further refinement of the model: incorporate target mobility The graph topology changes with time What are the complexity issues when online distributed algorithms are used? IISI, Cornell University

Purely Local Computation Models We are also exploring local computation methods for target tracking. (I.e. communication cannot be used for global computation.) We are drawing on an analogy to physical models. (energy function minimization approach) IISI, Cornell University

Summary

Introduced graph-based models capturing the ANTs challenge domain Results on the tradeoffs between: Computation, Communication, Radar range, and Performance. Results enable a more principled and efficient design of distributed sensor networks. Extensions: additional structural issues for the sensor domain complexity issues in distributed and dynamic settings IISI, Cornell University

Collaborations / Interactions ISI: Analytic Tools to Evaluate Negotiation Difficulty Design and evaluation of SAT encodings for CAMERA’s scheduling task. ISI: DYNAMITE Formal complexity analysis DCSP model (e.g., characterization of tractable subclasses). UMASS: Scalable RT Negotiating Toolkit Analysis of complexity of negotiation protocols.

The End IISI, Cornell University