Linear time local approximation algorithm for maximum stable marriage (Q1736578)

Summary: 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 \textit{E. McDermid} [Lect. Notes Comput. Sci. 5555, 689--700 (2009; Zbl 1248.68564)]. 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 \textit{K. Paluch} [Lect. Notes Comput. Sci. 7164, 176--187 (2012; Zbl 1242.68371)]. 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.