Abstract
A time efficient distributed algorithm for computing all maximal cliques in an arbitrary network is presented that is time efficient for every class of networks with a polynomial number of maximal cliques. The algorithm makes use of the algebraic properties of bipartite cliques which form a lattice structure. Assuming that it takes unit time to transmit the message of length \(\mathcal{O}\)(log n) bits, the algorithm has a time complexity of \(\mathcal{O}\)(M n log n) where M is the number of maximal cliques, and n is the number of processors in the network. The communication complexity is \(\mathcal{O}\)(M2 n2log n) assuming message length is \(\mathcal{O}\)(log n) bits.
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