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Disjoint Stable Matchings in Linear Time
arXiv - CS - Data Structures and Algorithms Pub Date : 2020-11-26 , DOI: arxiv-2011.13248 Prajakta Nimbhorkar, Geevarghese Philip, Vishwa Prakash HV
arXiv - CS - Data Structures and Algorithms Pub Date : 2020-11-26 , DOI: arxiv-2011.13248 Prajakta Nimbhorkar, Geevarghese Philip, Vishwa Prakash HV
We show that given a SM instance G as input we can find a largest collection
of pairwise edge-disjoint stable matchings of G in time linear in the input
size. This extends two classical results: 1. The Gale-Shapley algorithm, which can find at most two ("extreme")
pairwise edge-disjoint stable matchings of G in linear time, and 2. The polynomial-time algorithm for finding a largest collection of pairwise
edge-disjoint perfect matchings (without the stability requirement) in a
bipartite graph, obtained by combining K\"{o}nig's characterization with
Tutte's f-factor algorithm.
中文翻译:
线性时间中不相交的稳定匹配
我们表明,给定一个SM实例G作为输入,我们可以在输入大小的时间线性范围内找到G的成对边不相交稳定匹配的最大集合。这扩展了两个经典结果:1. Gale-Shapley算法,它最多可以在线性时间内找到G的两个(“极端”)成对边不相交的稳定匹配,以及2.用于找到最大集合的多项式时间算法通过将Kn“ nig的特征与Tutte的f因子算法相结合获得的二部图中成对的边不相交的完美匹配(无稳定性要求)。
更新日期:2020-12-01
中文翻译:
线性时间中不相交的稳定匹配
我们表明,给定一个SM实例G作为输入,我们可以在输入大小的时间线性范围内找到G的成对边不相交稳定匹配的最大集合。这扩展了两个经典结果:1. Gale-Shapley算法,它最多可以在线性时间内找到G的两个(“极端”)成对边不相交的稳定匹配,以及2.用于找到最大集合的多项式时间算法通过将Kn“ nig的特征与Tutte的f因子算法相结合获得的二部图中成对的边不相交的完美匹配(无稳定性要求)。