A fast algorithm to calculate powers of a Boolean matrix for diameter computation of random graphs

Authors:
Md. Abdur Razzaque;Choong Seon Hong;M. Abdullah-Al-Wadud;Oksam Chae
Affiliations:
Department of Computer Engineering, Kyung Hee University, Yongin-si, Gyonggi-do, South Korea;Department of Computer Engineering, Kyung Hee University, Yongin-si, Gyonggi-do, South Korea;Department of Computer Engineering, Kyung Hee University, Yongin-si, Gyonggi-do, South Korea;Department of Computer Engineering, Kyung Hee University, Yongin-si, Gyonggi-do, South Korea
Venue:
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
Year:
2008

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Abstract

In this paper, a fast algorithm is proposed to calculate kth power of an n × n Boolean matrix that requires O(kn3p) 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 Ak-1 and adds them up for calculating corresponding entries of Ak. 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(n2(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.