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Exploiting a Hypergraph Model for Finding Golomb Rulers

  • Manuel Sorge
  • Hannes Moser
  • Rolf Niedermeier
  • Mathias Weller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

Abstract

Golomb rulers are special rulers where for any two marks it holds that the distance between them is unique. They find applications in positioning of radio channels, radio astronomy, communication networks, and bioinformatics. An important subproblem in constructing “compact” Golomb rulers is Golomb Subruler (GSR), which asks whether it is possible to make a given ruler Golomb by removing at most k marks. We initiate a study of GSR from a parameterized complexity perspective. In particular, we develop a hypergraph characterization of rulers and consider the construction and structure of the corresponding hypergraphs. We exploit their properties to derive polynomial-time data reduction rules that lead to a problem kernel for GSR with O(k 3) marks. Finally, we provide a simplified NP-hardness construction for GSR.

Keywords

Hitting Set NP-Hardness Parameterized Complexity Data Reduction Problem Kernel Forbidden Subgraph Characterization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Manuel Sorge
    • 1
  • Hannes Moser
    • 1
  • Rolf Niedermeier
    • 1
  • Mathias Weller
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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