A Hypergraph Separator Based Variable Ordering Heuristic for Solving Real World SAT

Abstract

Problem structure has been used to guide the variable ordering heuristic in backtracking search since [1]. Recent experimental results show that guiding the variable ordering heuristic using tree decompositions can improve the performance of SAT and CSP solvers. Huang and Darwiche’s [2] variable ordering heuristic uses a Dtree, a static binary tree decomposition, to compute the variable group ordering. Since the Dtree has to be constructed before search, the pre-established variable groupings never change during the execution of the solving. Boolean Constraint Propagation (BCP) is the look-ahead strategy for all of the cutting-edge SAT solvers. Because long implication chains exist in real world instances and a large number of variables on the implication chains can be instantiated after making a relatively small number of decisions, the internal structure of real world instances often changes dramatically in different parts of the search tree.