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Local Search for Distributed SAT

This paper discusses a distributed SAT problem where a group of agents collaborate to find a solution. It introduces the Basic and Enhanced Distributed Breakout algorithms, as well as Multi-DB, which incorporates local search techniques and termination detection. Advantages and drawbacks are analyzed.

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Local Search for Distributed SAT

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  1. Local Search for Distributed SAT JIN Xiaolong (Based on [1] )

  2. Distributed SAT • A SAT problem: ,where • n variables, m clauses; • A group of agents: a1, a2,…, ah, each agent is responsible for: • a set of variables; • all clauses related to these variables; • (Note: a clauses may be related to several agents;) • A solution state is, for each agent ai : • all its variables have been set a truth value; • the truth values of all its clauses are true;

  3. Basic Distributed Breakout a communication network of agents a four-stages cycle each agent performs

  4. Basic Distributed Breakout (2) • An agent corresponds to: • a variable; • a group of constraints related to this variable; • eval: calculate the sum of the weights of all violated constraints based on the variables’ values in the received ‘Ok?’ messages; • improve: the maximal improvement by changing its variable’s value; • A quasi-local-minimum is: • eval > 0 ; • improve = 0 ; • all neighbors’ improve <= 0 ; • Update the weights of the constraints, if quasi-local-minimum;

  5. Enhanced Distributed Breakout ---Multi-DB • Each agent ai represents: • A group of variables; • All clauses related to these variables; • Each agent try to make all its clauses true; • Local search techniques was used by agent ai to select variables to flip: • WalkSAT; • Restart; • Tabu list; • Embeded termination detection;

  6. Features of Multi-DB • Distributed: variable & clause; • Each agent represents a group of variables; • Local evaluation (based on the local information); • Weighting technique (based on quasi local minimum); • Build-in termination detection;

  7. Advantages & Drawbacks • Advantages: • Highly distributed; • Drawbacks: • Higher communication cost ; • Slower speed: cycle & flip;

  8. References [1]. Local Search for Distributed SAT with Complex Local Problems, by K. Hirayama & M. Yokoo, in: Proceedings of the First International Joint Conference on Autonomous Agent & Multiagent Systems, Bologna, Italy, July 2002. [2]. Distributed Breakout Algorithm for Solving Distributed Constraint Satisfaction Problems, by M. Yokoo & K. Hirayama, in: Proceedings of the Second International Conference on Multiagent Systems, 1996.

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