Probe matrix problems: Totally balanced matrices

Abstract

Let M be a class of 0/1-matrices. A 0/l/*-matrix A where the *s induce a submatrix is a probe matrix of M if the *s in A can be replaced by Os and Is such that A becomes a member of M. We show that for M being the class of totally balanced matrices, it can be decided in polynomial time whether A is a probe totally balanced matrix. On our route toward proving this main result, we also prove that so-called partitioned probe strongly chordal graphs and partitioned probe chordal bipartite graphs can be recognized in polynomial time. © Springer-Verlag Berlin Heidelberg 2007.