On bounded block decomposition problems for under-specified systems of equations

M.J. Bomhoff, Walter Kern, Georg J. Still

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When solving a system of equations, it can be beneficial not to solve it in its entirety at once, but rather to decompose it into smaller subsystems that can be solved in order. Based on a bisimplicial graph representation we analyze the parameterized complexity of two problems central to such a decomposition: The Free Square Block problem related to finding smallest subsystems that can be solved separately, and the Bounded Block Decomposition problem related to determining a decomposition where the largest subsystem is as small as possible. We show both problems to be W[1]-hard. Finally we relate these problems to crown structures and settle two open questions regarding them using our results.
Original languageEnglish
Pages (from-to)336-347
Number of pages12
JournalJournal of computer and system sciences
Issue number1
Publication statusPublished - Jan 2012


  • Parameterized complexity
  • Decomposition
  • Bipartite graph


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