Generalized Satisfiability with Limited Occurrences per Variable: A Study through Delta-Matroid Parity

  • Victor Dalmau
  • Daniel K. Ford
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


In this paper we examine generalized satisfiability problems with limited variable occurrences. First, we show that 3 occurrences per variable suffice to make these problems as hard as their unrestricted version. Then we focus on generalized satisfiability problems with at most 2 occurrences per variable. It is known that some NP -complete generalized satisfiability problems become polynomially solvable when only 2 occurrences per variable are allowed. We identify two new families of generalized satisfiability problems, called local and binary, that are polynomially solvable when only 2 occurrences per variable are allowed. We achieve this result by means of a reduction to the \(\triangle\)-matroid parity problem, which is another important theme of this work.


Polynomial Time Atomic Formula Graph Match Local Path Variable Occurrence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Victor Dalmau
    • 1
  • Daniel K. Ford
    • 2
  1. 1.Universitat Pompeu Fabra 
  2. 2.UC Santa Cruz 

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