Fast Distributed Almost Stable Matchings
Fast Distributed Almost Stable Matchings
复制标题
快速分布式几乎稳定的匹配
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Will Rosenbaum
中科院分区：
文献类型：
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作者：
R. Ostrovsky;Will Rosenbaum
在他们关于稳定婚姻问题的开创性工作中，Gale和Shapley描述了一种算法，该算法在O（n2）通信回合中找到稳定匹配。他们的算法有一个自然的解释，作为一个分布式算法，其中每个球员是由一个单一的处理器表示。在这个分布式模型中，Floreen，Kaski，Polishchuk和Suomela最近表明，对于有界偏好列表，在恒定轮数后终止Gale-Shapley算法会导致几乎稳定的匹配。在本文中，我们描述了一个新的确定性分布式算法，发现一个几乎稳定的匹配在O（log 5 n）通信轮任意偏好。我们还提出了一个更快的随机变量，需要O（log 2 n）轮。对于“几乎规则”（特别是完全）的偏好，这个运行时间可以改进为O（1）轮。据我们所知，这些是第一次多项式轮分布式算法的任何变种的稳定的婚姻问题与无限的偏好。
In their seminal work on the Stable Marriage Problem, Gale and Shapley describe an algorithm which finds a stable matching in O(n2) communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each player is represented by a single processor. In this distributed model, Floreen, Kaski, Polishchuk, and Suomela recently showed that for bounded preference lists, terminating the Gale-Shapley algorithm after a constant number of rounds results in an almost stable matching. In this paper, we describe a new deterministic distributed algorithm which finds an almost stable matching in O(log5 n) communication rounds for arbitrary preferences. We also present a faster randomized variant which requires O(log2 n) rounds. This run-time can be improved to O(1) rounds for "almost regular" (and in particular complete) preferences. To our knowledge, these are the first sub-polynomial round distributed algorithms for any variant of the stable marriage problem with unbounded preferences.