![]() Unfortunately, the problem remains intractable even for the combined parameter k+t+d. We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list. In particular, the goal is to find a matching whose size exceeds that of a stable matching in the graph by at least t and has at most k blocking edges. In this paper, we study the question of matching more agents with fewest possible blocking edges. ![]() In light of the Rural Hospital Theorem, we have to relax the "no blocking pair" condition for stable matchings in order to match more agents. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. However, this need not be true when preference lists are incomplete. ![]() In the Stable Marriage problem, when the preference lists are complete, all agents of the smaller side can be matched.
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