Computational complexity of some restricted instances of 3-SAT

Piotr Berman, Marek Karpinski, Alexander D. Scott

    Research output: Contribution to journalArticlepeer-review

    9 Scopus citations

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)649-653
    Number of pages5
    JournalDiscrete Applied Mathematics
    Volume155
    Issue number5
    DOIs
    StatePublished - Mar 15 2007

    All Science Journal Classification (ASJC) codes

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics

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