Probe Matrix Problems: Totally Balanced Matrices

  • David B. Chandler
  • Jiong Guo
  • Ton Kloks
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4508)


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


Polynomial Time Bipartite Graph Chordal Graph Perfect Graph Probe Graph 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • David B. Chandler
    • 1
  • Jiong Guo
    • 2
  • Ton Kloks
    • 3
  • Rolf Niedermeier
    • 2
  1. 1.Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716 
  2. 2.Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 JenaGermany
  3. 3.School of Computing, University of Leeds, Leeds LS2 9JTUK

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