Algorithms and Implementation for Interconnection Graph Problem

Authors:
Hongbing Fan;Christian Hundt;Yu-Liang Wu;Jason Ernst
Affiliations:
Wilfrid Laurier University, Waterloo, Canada N2L3C5;University of Rostock, Germany;The Chinese University of Hong Kong, Shatin, N.T., Hong Kong,;University of Guelph, Guelph, Canada N1G2W1
Venue:
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Year:
2008

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Abstract

The Interconnection Graph Problem (IGP) is to compute for a given hypergraph H= (V, R) a graph G= (V, E) with the minimum number of edges |E| such that for all hyperedges N驴 Rthe subgraph of Ginduced by Nis connected. Computing feasible interconnection graphs is basically motivated by the design of reconfigurable interconnection networks. This paper proves that IGP is NP-complete and hard to approximate even when all hyperedges of Hhave at most three vertices. Afterwards it presents a search tree based parameterized algorithm showing that the problem is fixed-parameter tractable when the hyperedge size of His bounded. Moreover, the paper gives a reduction based greedy algorithm and closes with its experimental justification.