Optimal Self Routing of Linear Complement Permutations in Hypercubes

In this paper we describe an algorithm to route the class of linear complement permutations on Hy percube SIMD computers The class of linear complement permutations are extremely useful in de vising storage schemes for parallel array access The proposed algorithm is self routing and minimal that is the path established by the algorithm between each pair of source and destination processors is via a min imal path using only the destination processor ad dress Furthermore the algorithm requires only the optimal number of routing steps to realize any linear complement permutation The best known previous routing algorithms for the Hypercubes are for the class of bit permute complement permutations a subset of the class of linear complement permutations Those algorithms are either non optimal or not self routing The algorithm presented is self routing optimal and it routes a larger class of permutations Also this algo rithm can route the class of linear complement permu tations in multi dimensional meshes in optimal num ber of routing steps