日時
2014年1月15日(水) 16:30 ～ 17:30
場所
東大理学部7号館007号室（地下１階）および NII、東北大学でのポリコム中継
16:30 ～ 17:30
講演者
Chien-Chung Huang 先生 (Max-Planck-Institut für Informatik)
タイトル
Stability and popularity in matchings: a case study in the roommate problem
アブストラクト
Our input is a graph G = (V, E) where each vertex ranks its neighbors in a strict order of preference. The problem is to compute a matching in G that captures the preferences of the vertices in a popular way. Matching M is more popular than matching M’ if the number of vertices that prefer M to M’ is more than those that prefer M’ to M. The unpopularity factor of M measures by what factor any matching can be more popular than M. We show that G always admits a matching whose unpopularity factor is O(log|V|), and such a matching can be computed in linear time. In our problem the optimal matching would be a least unpopularity factor matching. We will show that computing such a matching is NP-hard. In fact, for any $epsilon$, it is NP-hard to compute a matching whose unpopularity factor is at most $4/3 -epsilon$ of the optimal.
