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Maximum Locally Stable Matchings
Algorithms 2013, 6(3), 471-484; doi:10.3390/a6030471

Linear Time Local Approximation Algorithm for Maximum Stable Marriage

Department of Computer Science and MTA-ELTE Egerváry Research Group, Eötvös University, Pázmány Péter sétany 1/C, Budapest 1117, Hungary
Received: 1 August 2013 / Revised: 6 August 2013 / Accepted: 7 August 2013 / Published: 15 August 2013
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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We consider a two-sided market under incomplete preference lists with ties, where the goal is to find a maximum size stable matching. The problem is APX-hard, and a 3/2-approximation was given by McDermid [1]. This algorithm has a non-linear running time, and, more importantly needs global knowledge of all preference lists. We present a very natural, economically reasonable, local, linear time algorithm with the same ratio, using some ideas of Paluch [2]. In this algorithm every person make decisions using only their own list, and some information asked from members of these lists (as in the case of the famous algorithm of Gale and Shapley). Some consequences to the Hospitals/Residents problem are also discussed.
Keywords: stable marriage; Gale-Shapley algorithm; approximation; Hospitals/Residents problem stable marriage; Gale-Shapley algorithm; approximation; Hospitals/Residents problem
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Király, Z. Linear Time Local Approximation Algorithm for Maximum Stable Marriage. Algorithms 2013, 6, 471-484.

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