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A distributed algorithm for finding Hamiltonian cycles in random graphs in O(log⁡n) time
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-09-14 , DOI: 10.1016/j.tcs.2020.09.020
Volker Turau

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=(logn+loglogn+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(logn) rounds. The algorithm works in the synchronous model and uses messages of size O(logn) and O(logn) memory per node.



中文翻译:

在随机图中查找哈密顿环的分布式算法。 Ø日志ñ 时间

一段时间以来,人们都知道随机图 Gñp如果p大于临界值,则包含汉密尔顿周期pC[R一世Ť=日志ñ+日志日志ñ+ωñ/ñ。确定混凝土的哈密顿循环Gñp即使p大于pC[R一世Ť。在本文中,我们考虑随机图Gñpp inΩ1个/ñ,在哪里 Ω隐藏n中的多对数因子。对于p的这个范围,我们提出一种分布式算法一种HC 发现w在哈密顿周期 Ø日志ñ回合。该算法在同步模型中工作,并使用大小不一的消息Ø日志ñØ日志ñ 每个节点的内存。

更新日期:2020-10-30
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