TY - JOUR

T1 - Computational complexity of some restricted instances of 3-SAT

AU - Berman, Piotr

AU - Karpinski, Marek

AU - Scott, Alexander D.

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007/3/15

Y1 - 2007/3/15

N2 - Tovey [A simplified satisfiability problem, Discrete Appl. Math. 8 (1984) 85-89] showed that it is NP-hard to decide the satisfiability of 3-SAT instances in which every variable occurs four times, while every instance of 3-SAT in which each variable occurs three times is satisfiable. We explore the border between these two problems. Answering a question of Iwama and Takaki, we show that, for every fixed k ≥ 0, there is a polynomial-time algorithm to determine the satisfiability of 3-SAT instances in which k variables occur four times and the remaining variables occur three times. On the other hand, it is NP-hard to decide the satisfiability of 3-SAT instances in which all but one variable occurs three times, and the remaining variable is allowed to occur an arbitrary number of times.

AB - Tovey [A simplified satisfiability problem, Discrete Appl. Math. 8 (1984) 85-89] showed that it is NP-hard to decide the satisfiability of 3-SAT instances in which every variable occurs four times, while every instance of 3-SAT in which each variable occurs three times is satisfiable. We explore the border between these two problems. Answering a question of Iwama and Takaki, we show that, for every fixed k ≥ 0, there is a polynomial-time algorithm to determine the satisfiability of 3-SAT instances in which k variables occur four times and the remaining variables occur three times. On the other hand, it is NP-hard to decide the satisfiability of 3-SAT instances in which all but one variable occurs three times, and the remaining variable is allowed to occur an arbitrary number of times.

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U2 - 10.1016/j.dam.2006.07.009

DO - 10.1016/j.dam.2006.07.009

M3 - Article

AN - SCOPUS:33846820200

VL - 155

SP - 649

EP - 653

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 5

ER -