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Optimal 2-constraint satisfaction via sum-product algorithms. (English) Zbl 1186.68439
Summary: We show that for a given set of \(m\) pairwise constraints over \(n\) variables, a variable assignment that satisfies maximally many \(m\) constraints (MAX-2-CSP) can be found in \(O^{\ast}(nmd^{n\omega/3})\) time, where \(d\) is the maximum number of states per variable, and \(\omega <2.376\) is the matrix product exponent over a ring; the notation \(O^{*}\) suppresses factors polylogarithmic in \(m\) and \(n\). As a corollary, MAX-2-SAT can be solved in \(O^{*}(nm1.732^n)\) time. This improves on a recent result by R. Williams [“A new algorithm for optimal 2-constraint satisfaction and its implications”, Theor. Comput. Sci. 348, No. 2–3, 357–365 (2005; Zbl 1081.68095)] by reducing the polynomial factor from \(nm^{3}\) to about \(nm\).

MSC:
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
68Q25 Analysis of algorithms and problem complexity
Software:
MAX-2-SAT
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