An Efficient Algorithm for Batch Stability Testing

Given a stable marriage problem instance represented by a bipartite graph having 2n vertices and m edges, we describe an algorithm that can verify the stability of k different matchings in a batch fashion in O((m + kn) log2 n) time. This affirmatively answers a longstanding open question of Gusfield and Irving as to whether stability can be verified in a batch setting (after sufficient preprocessing) in time sub-quadratic in n.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: John Dabney, Brian C. Dean
• Keywords: ALGORITHMICA 2010, Bipartite Graph, Longstanding Open Question, Marriage Problem Instance