TY - JOUR

T1 - Approximating Max NAE-k-SAT by anonymous local search

AU - Xian, Aiyong

AU - Zhu, Kaiyuan

AU - Zhu, Daming

AU - Pu, Lianrong

AU - Liu, Hong

N1 - Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2017/1/2

Y1 - 2017/1/2

N2 - A clause is not-all-equal satisfied if it has at least one literal assigned with true and one literal assigned with false. Max NAE-SAT is given by a boolean variable set U and a clause set C, asks to find an assignment of U, such that the number of not-all-equal satisfied clauses in C is maximized. Max NAE-SAT turns into Max NAE-k-SAT if each clause contains exactly k literals. Local search has long been used in various SAT solvers. However, little has been done on local search to approximate Max NAE-k-SAT. Moreover, it is still open for what a quantitative bound could Max NAE-k-SAT be approximated to, at best. In this paper, we propose a local search algorithm which can approximate Max NAE-k-SAT to [formula presented] for each fixed k≥2. Then we show that Max NAE-k-SAT cannot be approximated within [formula presented] in polynomial time, if P≠NP. The algorithm for Max NAE-k-SAT can be extended to approximate Max NAE-SAT where each clause contains at least k literals to [formula presented]. Using the algorithm for Max NAE-SAT where each clause contains at least k literals, we present a new algorithm to approximate Max-SAT where each clause contains at least k literals to [formula presented].

AB - A clause is not-all-equal satisfied if it has at least one literal assigned with true and one literal assigned with false. Max NAE-SAT is given by a boolean variable set U and a clause set C, asks to find an assignment of U, such that the number of not-all-equal satisfied clauses in C is maximized. Max NAE-SAT turns into Max NAE-k-SAT if each clause contains exactly k literals. Local search has long been used in various SAT solvers. However, little has been done on local search to approximate Max NAE-k-SAT. Moreover, it is still open for what a quantitative bound could Max NAE-k-SAT be approximated to, at best. In this paper, we propose a local search algorithm which can approximate Max NAE-k-SAT to [formula presented] for each fixed k≥2. Then we show that Max NAE-k-SAT cannot be approximated within [formula presented] in polynomial time, if P≠NP. The algorithm for Max NAE-k-SAT can be extended to approximate Max NAE-SAT where each clause contains at least k literals to [formula presented]. Using the algorithm for Max NAE-SAT where each clause contains at least k literals, we present a new algorithm to approximate Max-SAT where each clause contains at least k literals to [formula presented].

KW - Algorithm

KW - Complexity

KW - Local search

KW - Performance ratio

KW - Satisfiability

UR - http://www.scopus.com/inward/record.url?scp=84973457813&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2016.05.040

DO - 10.1016/j.tcs.2016.05.040

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AN - SCOPUS:84973457813

SN - 0304-3975

VL - 657

SP - 54

EP - 63

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -