Probe Matrix Problems: Totally Balanced Matrices

David B. Chandler, Jiong Guo, Ton Kloks, Rolf Niedermeier

Abstract: Let be a class of 0/1-matrices. A 0/1/ ⋆-matrix A where the ⋆s induce a submatrix is a probe matrix of  if the ⋆s in A can be replaced by 0s and 1s such that A becomes a member of . We show that for 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.