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.