Probe Matrix Problems: Totally Balanced Matrices

Authors:
David B. Chandler;Jiong Guo;Ton Kloks;Rolf Niedermeier
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716,;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;School of Computing, University of Leeds, Leeds LS2 9JT, UK;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany
Venue:
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Year:
2007

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Abstract

Let be a class of 0/1-matrices. A 0/1/ 茂戮驴-matrix Awhere the 茂戮驴s induce a submatrix is a probe matrixof if the 茂戮驴s in Acan be replaced by 0s and 1s such that Abecomes a member of . We show that for being the class of totally balanced matrices, it can be decided in polynomial time whether Ais 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.