One more occurrence of variables makes satisfiability jump from trivial to NP-complete

Jan Kratochvil, Petr Savicky, Zsolt Tuza

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

A Boolean formula in a conjunctive normal form is called a (k, s) - formula if every clause contains exactly k variables and every variable occurs in at most s clauses. The (k,s) -- SAT problem is the SATISFIABILITY problem restricted to (k,s) -- formulas. It is proved that for every k ≥ 3 there is an integer f(k) such that (k, s) -- SAT is trivial for s ≤ f(k) (because every (k, s) -- formula is satisfiable) and is NP-complete for s ≥ f(k) + 1. Moreover, f(k) grows exponentially with k, namely, [2k/ck] ≤ f(k) ≤ 2k-1 - 2k-4 - 1 for k ≥ 4.

Original languageEnglish
Pages (from-to)203-210
Number of pages8
JournalSIAM Journal on Computing
Volume22
Issue number1
DOIs
Publication statusPublished - Jan 1 1993

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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