The Worst-Case Upper Bound for Exact 3-Satisfiability with the Number of Clauses as the Parameter

Zhou, Junping; Yin, Minghao

doi:10.1007/978-3-642-29700-7_20

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…Surprisingly, there are only few algorithms for which the complexity is computed in terms of the number of clauses M. Among them, Skjernaa presented an algorithm for XSAT with a time bound ( ) O 2 M , but using exponential space [22]. A better algorithm which uses polynomial space and time ( ) O 2 M 0.2123 has been provided by Zhou and Yin [23]. Excluding the algorithm by Schroeppel and Shamir [17], all the algorithms mentioned above are branch-and-reduce algorithms, which means that the variables (or alternatively the clauses) are iteratively removed before a reduction step [24,25].…”

Section: Introductionmentioning

confidence: 99%

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

2016

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We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by ( ) ¢ -O 2 n M and ( ) ¢ -

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Section: Introductionmentioning

confidence: 99%

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

2016

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“…Given a 2-CF F with n variables and m clauses, it is common to analyze the computational complexity of the algorithms for solving #2SAT and #2UNSAT regarding to n or m or any combination of both [10,11].…”

Section: Introductionmentioning

confidence: 99%

Computing #2SAT and #2UNSAT by Binary Patterns

Luna¹,

Marcial‐Romero

2012

Lecture Notes in Computer Science

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We present some results about the parametric complexity of #2SAT and #2UNSAT, which consist on counting the number of models and falsifying assignments, respectively, for two Conjunctive Forms (2-CF's). Firstly, we show some cases where given a formula F , #2SAT(F) can be bounded above by considering a binary pattern analysis over its set of clauses. Secondly, since #2SAT(F) = 2 n-#2UNSAT(F) we show that, by considering the constrained graph GF of F , if GF represents an acyclic graph then, #UNSAT(F) can be computed in polynomial time. To the best of our knowledge, this is the first time where #2UNSAT is computed through its constrained graph, since the inclusion-exclusion formula has been commonly used for computing #UNSAT(F).

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The Worst-Case Upper Bound for Exact 3-Satisfiability with the Number of Clauses as the Parameter

Cited by 2 publications

References 7 publications

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

Computing #2SAT and #2UNSAT by Binary Patterns

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