Communication and Computation in DCSP Algorithms
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1 Communication and Computation in DCSP Algorithms Universitat de Lleida Cèsar Fernàndez Ramón Béjar.. Intelligent Information Systems Institute CORNELL Bhaskar Krishnamachari Carla Gomes September, 10th 2002
2 Testing DisCSP algorithms in real environments Testing DisCSP algorithms in real environments The need for realistic DisCSP benchmarks We need problem instances that capture the structure of real DisCSP But we need an easy way to generate instances with different constrainedness Our proposal: a distributed resource allocation problem The effect of the communication network In real scenarios, agents will experience the delays of the communication network We should investigate how delays affect the performance of the algorithms Our proposal: a discrete event-simulator able to simulate different delay distributions 1
3 Testing DisCSP algorithms in real environments DisCSP SensorDCSP benchmark DisCSP algorithms Complexity profiles of DisCSP algorithms on SensorDCSP The effect of the communication network load Delays actively added by the Agents Delays because of the network load 2
4 Distributed Constraint Satisfaction Problem (DisCSP) Distributed Constraint Satisfaction Problem (DisCSP) Agents need to solve different CSPs Local constraints (within Agents) Global constraints (between Agents) How do Agents solve it? Local constraints: computation Global constraints: computation + communication What is the impact of the communication network in the performance? 3
5 SensorDCSP benchmark SensorDCSP benchmark Input: Multiple sensors (s i ) and mobiles (t j ) randomly scattered Constraints: sensor visibility bipartite graph (P v ): sensors that can track a given mobile every sensor can track at most one mobile sensor compatibility graph (P c ): compatibility relation between sensors Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it. s 1 t 1 s 2 s 3 s 5 t 2 s 4 s 6. 4
6 SensorDCSP benchmark SensorDCSP benchmark Input: Multiple sensors (s i ) and mobiles (t j ) randomly scattered Constraints: sensor visibility bipartite graph (P v ): sensors that can track a given mobile every sensor can track at most one mobile sensor compatibility graph (P c ): compatibility relation between sensors Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it. s 1 t 1 s 2 s 3 s 5 t 2 s 4 s 6. 5
7 SensorDCSP benchmark SensorDCSP benchmark Input: Multiple sensors (s i ) and mobiles (t j ) randomly scattered Constraints: sensor visibility bipartite graph (P v ): sensors that can track a given mobile every sensor can track at most one mobile sensor compatibility graph (P c ): compatibility relation between sensors Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it. s 1 t 1 s 2 s 3 s 5 t 2 s 4 s 6. 6
8 SensorDCSP benchmark SensorDCSP benchmark Input: Multiple sensors (s i ) and mobiles (t j ) randomly scattered Constraints: sensor visibility bipartite graph (P v ): sensors that can track a given mobile every sensor can track at most one mobile sensor compatibility graph (P c ): compatibility relation between sensors Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it. s 1 t 1 s 2 s 3 s 5 t 2 s 4 s 6. 7
9 DisCSP algorithms DisCSP algorithms Messages exchanged: Ok: inform about assignments to its neighbors nogood: ask a neighbor to change its assignment Algorithms: Asynchronous Backtracking (ABT) static ordering between agents random selection among values consistent with higher (priority) agents Asynchronous Weak-Commitment Search (AWC) dynamic priority ordering random selection among values consistent with higher agents and that minimize constraint violations with lower agents Implemented using a distributed discrete-event network simulator 8
10 Complexity profiles of DisCSP algorithms on SensorDCSP Complexity profiles of DisCSP algorithms on SensorDCSP Experimental scenario Inter-agent communication delays: exponentially distributed, mean 1 time unit 3 mobiles and 15 sensors. P c and P v ranging from 0.1 to instances per point. 9 independent runs for instance Ratio of satisfiable instances P sat P v 0.8 P c 9
11 Complexity profiles of DisCSP algorithms on SensorDCSP Mean solution time Time units AWC P c P v 0.8 P sat = 0.8 P sat = 0.2 Time units ABT NP-complete for P c < 1 harder for lower P c 0.8 P c P v
12 Restarting strategy for ABT Restarting strategy for ABT Higher priority agent initiates the restarting of the search Performance depends on cutoff time Not suitable for AWC due to its inherent dynamic priority behavior Mean solution time on a hard instance 120 ABT with restarting 110 Time units Cutoff time units 11
13 Active delaying of messages Active delaying of messages Adding delay introduces a controlled source of randomization. Controlling the level of randomization: p, probability that an agent adds extra delay 0 r 1, amount of added delay (fraction of the delay of the link) Median values for a hard instance (AWC in a fixed delay scenario) Time units Number of messages r p r p
14 The effect of the communication network load The effect of the communication network load Different traffic conditions modeled by different delay distributions Random delays impact algorithms performance in different ways: ABT: Fixed delays better than random delays. The greater the variance of the delays, the worse the performance of ABT ABT with restarting: Fairly robust to the variance of the delays AWC: Random delays better than fixed delays. Extremely robust to the variance of the delays 13
15 The effect of the communication network load Cumulative density functions of time to solve a hard instance (ABT) ABT CDF 0.01 Fixed Time units 14
16 The effect of the communication network load Cumulative density functions of time to solve a hard instance (ABT) ABT CDF 0.01 Fixed Negative Exponential (σ 2 = 1) Log-normal (σ 2 = 10) Time units 15
17 The effect of the communication network load Cumulative density functions of time to solve a hard instance (ABT) ABT CDF Fixed Negative Exponential (σ 2 = 1) Log-normal (σ 2 = 10) Neg. Exp. with restart (σ 2 = 1) Log-normal with restart (σ 2 = 10) Time units 16
18 The effect of the communication network load Cumulative density functions of time to solve a hard instance (AWC) AWC CDF 0.01 Fixed Time units 17
19 The effect of the communication network load Cumulative density functions of time to solve a hard instance (AWC) AWC CDF 0.01 Fixed Negative Exponential (σ 2 = 1) Time units 18
20 The effect of the communication network load Cumulative density functions of time to solve a hard instance (AWC) AWC CDF Fixed Negative Exponential (σ 2 = 1) Log-normal (σ 2 = 5) Log-normal (σ 2 = 10) Time units 19
21 Conclusions Conclusions Introduction of the SensorDCSP benchmark. Phase transition behavior in satisfiability. Constrainedness adjusted by the visibility and compatibility graphs Discrete-event simulator used to determine the impact of different network traffic conditions on the algorithms performance: ABT performance worse for random delays ABT improved using restarting AWC performance better for random delays. Robustness in front of large random delay variations AWC improved in fixed delay scenarios by the active addition of random delays 20
22 Conclusions Conclusions Introduction of the SensorDCSP benchmark. Phase transition behavior in satisfiability. Constrainedness adjusted by the visibility and compatibility graphs Discrete-event simulator used to determine the impact of different network traffic conditions on the algorithms performance: ABT performance worse for random delays ABT improved using restarting AWC performance better for random delays. Robustness in front of large random delay variations AWC improved in fixed delay scenarios by the active addition of random delays 20
23 Conclusions Conclusions Introduction of the SensorDCSP benchmark. Phase transition behavior in satisfiability. Constrainedness adjusted by the visibility and compatibility graphs Discrete-event simulator used to determine the impact of different network traffic conditions on the algorithms performance: ABT performance worse for random delays ABT improved using restarting AWC performance better for random delays. Robustness in front of large random delay variations AWC improved in fixed delay scenarios by the active addition of random delays 20
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