Classification of OBDD size for monotone 2-CNFs

Abstract

We introduce a new graph parameter called linear upper maximum induced matching width \textsc{lu-mim width}, denoted for a graph $G$ by $lu(G)$. We prove that the smallest size of the \textsc{obdd} for $\phi$, the monotone 2-\textsc{cnf} corresponding to $G$, is sandwiched between $2^{lu(G)}$ and $n^{O(lu(G))}$. The upper bound is based on a combinatorial statement that might be of an independent interest. We show that the bounds in terms of this parameter are best possible.

The presentation has been significantly improved. New material has been added: full proofs instead of sketches, examples with illustrations