Isomorphism of Conflict Graphs in Multistage Interconnection Networks and its Application to Optimal Routing

Authors:
Nabanita Das;Bhargab B. Bhattacharya;Jayasree Dattagupta
Affiliations:
Indian Statistical Institute, Calcutta, India;Indian Statistical Institute, Calcutta, India;Indian Statistical Institute, Calcutta, India
Venue:
IEEE Transactions on Computers
Year:
1993

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Abstract

A study on the isomorphism of conflict graphs in multistage interconnection networks (MINs) and its applications is outlined. A concept called group-transformation is introduced for the baseline network, which induces an equivalence partition on the set of all permutations. All members belonging to the same equivalence class have isomorphic conflict graphs. Thus, determination of conflict resolution of one permutation results in determination of conflict resolution of all other equivalent members. The BPCL (bit-permute-closure) class of permutations is defined, for which the conflict resolution problem can be settled in linear time by an earlier algorithm developed only for the BPC (bit-permute-complement) permutations. It is proved that for an N*N MIN, mod BPCL mod