## Abstract

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 V_{1}, V_{2}, . . ., V_{m} ⊆ V, and asks for a minimum-cardinality edge set E such that for the graph G = (V, E) all induced subgraphs G[V_{1}], G[V_{2}], . . ., G[V_{m}] 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 language | English |
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Pages (from-to) | 1-25 |

Number of pages | 25 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 29 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2015 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- General Mathematics