Publisher DOI: 10.1016/j.tcs.2020.09.020
Title: A distributed algorithm for finding Hamiltonian cycles in random graphs in O(log⁡n) time
Language: English
Authors: Turau, Volker 
Keywords: Distributed algorithm; Hamiltonian cycle; Random graph
Issue Date: Dec-2020
Source: Theoretical Computer Science 846: 61-74 (2020-12)
Abstract (english): 
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 pcrit=(log⁡n+log⁡log⁡n+ωn)/n. The determination of a concrete Hamiltonian cycle for G(n,p) is a nontrivial task, even when p is much larger than pcrit. In this paper we consider random graphs G(n,p) with p in Ω˜(1/n), where Ω˜ hides poly-logarithmic factors in n. For this range of p we present a distributed algorithm AHC that finds w.h.p. a Hamiltonian cycle in O(log⁡n) rounds. The algorithm works in the synchronous model and uses messages of size O(log⁡n) and O(log⁡n) memory per node.
ISSN: 0304-3975
Journal: Theoretical computer science 
Institute: Telematik E-17 
Document Type: Article
Project: Fehlertolerante Middleware-Idiome basierend auf selbststabilisierenden Techniken 
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