Popular Matchings under Matroid Constraints
نویسندگان
چکیده
In this paper, we consider a matroid generalization of the popular matching problem introduced by Abraham, Irving, Kavitha and Mehlhorn. We present a polynomial-time algorithm for this problem.
منابع مشابه
Stable Matchings with Ties, Master Preference Lists, and Matroid Constraints
In this paper, we consider a matroid generalization of the hospitals/residents problem with ties and master lists. In this model, the capacity constraints for hospitals are generalized to matroid constraints. By generalizing the algorithms of O’Malley for the hospitals/residents problem with ties and master lists, we give polynomial-time algorithms for deciding whether there exist a super-stabl...
متن کاملPareto Stable Matchings under One-Sided Matroid Constraints
The Pareto stability is one of solution concepts in two-sided matching markets with ties. It is known that there always exists a Pareto stable matching in the many-to-many setting. In this paper, we consider the following generalization of the Pareto stable matching problem in the many-to-many setting. Each agent v of one side has a matroid defined on the set of edges incident to v, and the set...
متن کاملEven Delta-Matroids and the Complexity of Planar Boolean CSPs
The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even ∆-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of pla...
متن کاملOn the maximum even factor in weakly symmetric graphs
As a common generalization of matchings and matroid intersection, W.H. Cunningham and J.F. Geelen introduced the notion of path-matchings, then they introduced the more general notion of even factor in weakly symmetric digraphs. Here we give a min-max formula for the maximum cardinality of an even factor. Our proof is purely combinatorial. We also provide a Gallai-Edmonds-type structure theorem...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS The Independent Even Factor Problem
Cunningham and Geelen (1997) introduced the notion of independent path-matchings, which generalize both matchings and matroid intersection. Path-matchings are yet generalized to even factors in digraphs by Cunningham and Geelen (2001). Pap (2005) gave a combinatorial algorithm to find a maximum even factor in odd-cycle-symmetric digraphs, in which each arc in any odd dicycle has the reverse arc...
متن کامل