Algorithms and Implementation for Interconnection Graph Problem
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 ∈ R the subgraph of G induced by N is 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 H have 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 H is bounded. Moreover, the paper gives a reduction based greedy algorithm and closes with its experimental justification.
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