Polynomial-time data reduction for the subset interconnection design problem

Jiehua Chen, Christian Komusiewicz, Rolf Niedermeier, Manuel Sorge, Ondřej Suchy, Mathias Weller

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The NP-hard SUBSET INTERCONNECTION DESIGN problem, also known as MINIMUM TOPIC-CONNECTED OVERLAY, is motivated by numerous applications including the design of scalable overlay networks and vacuum systems. It has as input a finite set V and a collection of subsets V1, V2, . . ., Vm ⊆ V, 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. We study SUBSET INTERCONNECTION DESIGN in the context of polynomial-time data reduction rules that preserve the possibility of constructing optimal solutions. Our contribution is threefold: First, we show the incorrectness of earlier polynomial-time data reduction rules. Second, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. Third, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. To achieve our results, we elaborate on polynomial-time data reduction rules which also may be of practical use in solving Subset Interconnection Design.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 1 Jan 2015
Externally publishedYes


  • Combinatorial algorithms
  • Fixed-parameter tractability
  • Hypergraph support
  • Kernelization
  • NP-hard problem
  • Preprocessing

ASJC Scopus subject areas

  • Mathematics (all)


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