Linear Time Local Approximation Algorithm for Maximum Stable Marriage

Algorithms

关键词: stable marriage;    Gale-Shapley algorithm;    approximation;    Hospitals/Residents problem;   

DOI  :  10.3390/a6030471

来源: mdpi

【 摘 要 】

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 -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.

【 授权许可】

CC BY   
© 2013 by the author; licensee MDPI, Basel, Switzerland.