Community Structure Inspired Algorithms for SAT and #SAT

• Published in: Theory and Applications of Satisfiability Testing -- SAT 2015 Vol. 9340; pp. 223 - 237
• Main Authors: Ganian, Robert, Szeider, Stefan
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2015; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Artificial intelligence; Community Structure; Computer science; Constraint Satisfaction Problem; Dual Graph; Equivalence Class; Mathematical theory of computation; Tree Decomposition
• ISBN: 3319243179; 9783319243177
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-24318-4_17

We introduce h-modularity, a structural parameter of CNF formulas, and present algorithms that render the decision problem SAT and the model counting problem #SAT fixed-parameter tractable when parameterized by h-modularity. The new parameter is defined in terms of a partition of clauses of the given CNF formula into strongly interconnected communities which are sparsely interconnected with each other. Each community forms a hitting formula, whereas the interconnections between communities form a graph of small treewidth. Our algorithms first identify the community structure and then use them for an efficient solution of SAT and #SAT, respectively. We further show that h-modularity is incomparable with known parameters under which SAT or #SAT is fixed-parameter tractable.