Disjoint Stable Matchings in Linear Time
@inproceedings{Nimbhorkar2020DisjointSM,
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},
year={2020}
}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…
One Citation
Diverse Non Crossing Matchings*
- Mathematics
- 2022
A perfect matching M on a set P of n points is a collection of line segments with endpoints from P such that every point belongs to exactly one segment. A matching is non-crossing if the line…
References
SHOWING 1-10 OF 18 REFERENCES
The number of disjoint perfect matchings in semi-regular graphs
- Mathematics
- 2017
We obtain a sharp result that for any even n ≥ 34, every {Dn,Dn+1}-regular
graph of order n contains ┌n/4┐ disjoint perfect matchings, where Dn =
2┌n/4┐-1. As a consequence, for any integer D ≥…
A simply exponential upper bound on the maximum number of stable matchings
- Mathematics, Computer ScienceSTOC
- 2018
It is shown that for all n, f(n) ≤ cn for some universal constant c, which matches the lower bound up to the base of the exponent.
The Geometry of Fractional Stable Matchings and Its Applications
- MathematicsMath. Oper. Res.
- 1998
It is shown that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions, which leads to a genuinely simple proof of the integrality of the stablemarriage polytopes.
The Complexity of Counting Stable Marriages
- MathematicsSIAM J. Comput.
- 1986
It is proved that the enumeration version of the problem—determining the number of stable matchings—is P-complete, and therefore cannot be solved in polynomial time if the search version ofThe problem is polynomially solvable.
A Short Proof of the Factor Theorem for Finite Graphs
- MathematicsCanadian Journal of Mathematics
- 1954
We define a graph as a set V of objects called vertices together with a set E of objects called edges, the two sets having no common element. With each edge there are associated just two vertices,…
The Stable marriage problem - structure and algorithms
- Computer ScienceFoundations of computing series
- 1989
The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a moregeneral set of problems.
The NP-Completeness of Edge-Coloring
- MathematicsSIAM J. Comput.
- 1981
It is shown that it is NP-complete to determine the chromatic index of an arbitrary graph, even for cubic graphs.