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- W2295763947 abstract "Counting models for two Conjunctive Normal Form formulae (2-CFs), known as the #2SAT problem, is a classic #P complete problem. It is known that if the constraint graph of a 2-CF F is acyclic or contains loops and parallel edges, $$#2SAT(F)$$ can be computed efficiently. In this paper we address the cyclic case different from loops and parallel edges. If the constraint graph G of a 2-CF F is cyclic, T a spanning tree plus loops and parallel edges of G and $$overline{T}=Gsetminus T$$ , what we called its cotree, we show that by building a set partition $$cup T_i$$ of $$overline{T}$$ , where each $$T_i$$ of the partition is formed by the frond edges of the cycles that are chained via other intersected cycles, then a parametric polynomial deterministic procedure for computing #2SAT with time complexity for the worst case of $$O(2^{k} cdot poly(|E(T)|))$$ can be obtained, where poly is a polynomial function, and k is the cardinality of the largest set in the partition. This method shows that #2SAT is in the class of fixed-parameter tratable (FPT) problems, where the fixed-parameter k in our proposal, depends on the number of edges of a subcotree of a decomposition of the constraint graph (tree+loops+parallel:cotree) associated to the formula." @default.
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- W2295763947 date "2015-01-01" @default.
- W2295763947 modified "2023-09-26" @default.
- W2295763947 title "A Parametric Polynomial Deterministic Algorithm for #2SAT" @default.
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- W2295763947 doi "https://doi.org/10.1007/978-3-319-27060-9_16" @default.
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