Disjoint Stable Matchings in Linear Time

  title={Disjoint Stable Matchings in Linear Time},
  author={Prajakta Nimbhorkar and Geevarghese Philip and Vishwa Prakash HV},
  booktitle={International Workshop on Graph-Theoretic Concepts in Computer Science},
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… 

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