On the Equivalence among Problems of Bounded Width

الأصل · EN

In this paper, we introduce a methodology, called decomposition-based reductions, for showing the equivalence among various problems of bounded-width. First, we show that the following are equivalent for any α> 0: * SAT can be solved in O*(2αtw) time, * 3-SAT can be solved in O*(2αtw) time, * Max 2-SAT can be solved in O*(2αtw) time, * Independent Set can be solved in O*(2αtw) time, and * Independent Set can be solved in O*(2αcw) time, where tw and cw are the tree-width and clique-width of the instance, respectively. Then, we introduce a new parameterized complexity class EPNL, which includes Set Cover and Directed Hamiltonicity, and show that SAT, 3-SAT, Max 2-SAT, and Independent Set parameterized by path-width are EPNL-complete. This implies that if one of these EPNL-complete problems can be solved in O*(cᵏ) time, then any problem in EPNL can be solved in O*(cᵏ) time.