A distributed algorithm for finding hamiltonian cycles in random graphs in O(Log n) time
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International Colloquium on Structural Information and Communication Complexity (SIROCCO 2018)
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It is known for some time that a random graph G(n, p) contains w.h.p. a Hamiltonian cycle if p is larger than the critical value (formula presented). The determination of a concrete Hamiltonian cycle is even for values much larger than p crit a nontrivial task. In this paper we consider random graphs G(n, p) with p in (formula presented), where (formula presented) hides poly-logarithmic factors in n. For this range of p we present a distributed algorithm A HC that finds w.h.p. a Hamiltonian cycle in O(logn) rounds. The algorithm works in the synchronous model and uses messages of size O(logn) and O(logn) memory per node.