Effective and Efficient Data Reduction for the Subset Interconnection Design Problem

  • Jiehua Chen
  • Christian Komusiewicz
  • Rolf Niedermeier
  • Manuel Sorge
  • Ondřej Suchý
  • Mathias Weller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

Abstract

The NP-hard Subset Interconnection Design problem is motivated by applications in designing vacuum systems and scalable overlay networks. It has as input a set V and a collection of subsets V1, V2, …, Vm, and asks for a minimum-cardinality edge set E such that for the graph G = (V,E) all induced subgraphs G[V1], G[V2], …, G[Vm] are connected. It has also been studied under the name Minimum Topic-Connected Overlay. We study Subset Interconnection Design in the context of polynomial-time data reduction rules that preserve optimality. Our contribution is threefold: First, we point out flaws in earlier polynomial-time data reduction rules. Second, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. Third, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. To achieve our results, we elaborate on polynomial-time data reduction rules (partly “repairing” previous flawed ones) which also may be of practical use in solving Subset Interconnection Design.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jiehua Chen
    • 1
  • Christian Komusiewicz
    • 1
  • Rolf Niedermeier
    • 1
  • Manuel Sorge
    • 1
  • Ondřej Suchý
    • 2
  • Mathias Weller
    • 3
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.Department of Theoretical Computer ScienceCzech Technical University in PragueCzech Republic
  3. 3.Département InformatiqueLIRMMFrance

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