A Fast Algorithm to Calculate Powers of a Boolean Matrix for Diameter Computation of Random Graphs
- Cite this paper as:
- Razzaque M.A., Hong C.S., Abdullah-Al-Wadud M., Chae O. (2008) A Fast Algorithm to Calculate Powers of a Boolean Matrix for Diameter Computation of Random Graphs. In: Nakano S., Rahman M.S. (eds) WALCOM: Algorithms and Computation. WALCOM 2008. Lecture Notes in Computer Science, vol 4921. Springer, Berlin, Heidelberg
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.
KeywordsBoolean Matrix Random Graphs Adjacency Matrix Graph Diameter Computational Complexity
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