A Fast Algorithm to Calculate Powers of a Boolean Matrix for Diameter Computation of Random Graphs

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Abstract

In this paper, a fast algorithm is proposed to calculate k th power of an n×n Boolean matrix that requires O(kn 3 p) addition operations, where p is the probability that an entry of the matrix is 1. The algorithm generates a single set of inference rules at the beginning. It then selects entries (specified by the same inference rule) from any matrix A k − 1 and adds them up for calculating corresponding entries of A k . No multiplication operation is required. A modification of the proposed algorithm can compute the diameter of any graph and for a massive random graph, it requires only O(n 2(1-p)E[q]) operations, where q is the number of attempts required to find the first occurrence of 1 in a column in a linear search. The performance comparisons say that the proposed algorithms outperform the existing ones.