Generalized satisfiability with limited occurrences per variable: A study through delta-matroid parity

Abstract

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 Δ-matroid parity problem, which is another important theme of this work. © Springer-Verlag Berlin Heidelberg 2003.