On Explaining Integer Vectors by Few Homogenous Segments

  • Robert Bredereck
  • Jiehua Chen
  • Sepp Hartung
  • Christian Komusiewicz
  • Rolf Niedermeier
  • Ondřej Suchý
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


We extend previous studies on NP-hard problems dealing with the decomposition of nonnegative integer vectors into sums of few homogeneous segments. These problems are motivated by radiation therapy and database applications. If the segments may have only positive integer entries, then the problem is called Vector Explanation  + . If arbitrary integer entries are allowed in the decomposition, then the problem is called Vector Explanation. Considering several natural parameterizations (including maximum vector entry, maximum difference between consecutive vector entries, maximum segment length), we obtain a refined picture of the computational (in-)tractability of these problems. In particular, we show that in relevant cases Vector Explanation  +  is algorithmically harder than Vector Explanation .


Integer Linear Program Intensity Modulate Radiation Therapy Integer Linear Program Formulation Solution Size Clean Position 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Robert Bredereck
    • 1
  • Jiehua Chen
    • 1
  • Sepp Hartung
    • 1
  • Christian Komusiewicz
    • 1
  • Rolf Niedermeier
    • 1
  • Ondřej Suchý
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.Faculty of Information TechnologyCzech Technical University in PragueCzech Republic

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