On explaining integer vectors by few homogenous segments

Authors:
Robert Bredereck;Jiehua Chen;Sepp Hartung;Christian Komusiewicz;Rolf Niedermeier;Ondřej Suchý
Affiliations:
Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Venue:
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Year:
2013

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Abstract

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 .