Probe matrix problems: Totally balanced matrices

Let M be a class of 0/1-matrices. A 0/1/*-matrix A where the *s induce a submatrix is a probe matrix of M if the *s in A can be replaced by 0s and 1s 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.