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

6/3/20152 Distributed SAT A SAT problem:,where –n variables, m clauses; A group of agents: a 1, a 2,…, a h, 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 a i : –all its variables have been set a truth value; –the truth values of all its clauses are true;

6/3/20153 Basic Distributed Breakout a four-stages cycle each agent performsa communication network of agents

6/3/20154 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;

6/3/20155 Enhanced Distributed Breakout Each agent a i 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 a i to select variables to flip: –WalkSAT; –Restart; –Tabu list; Embeded termination detection; ---Multi-DB

6/3/20156 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;

6/3/20157 Advantages & Drawbacks Advantages: –Highly distributed; Drawbacks: –Higher communication cost ; –Slower speed: cycle & flip;

6/3/20158 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 [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.