DeepAI AI Chat
Log In Sign Up

Approximation Algorithms for Matroidal and Cardinal Generalizations of Stable Matching

by   Gergely Csáji, et al.
National Institute of Informatics

The Stable Marriage problem (SM), solved by the famous deferred acceptance algorithm of Gale and Shapley (GS), has many natural generalizations. If we allow ties in preferences, then the problem of finding a maximum solution becomes NP-hard, and the best known approximation ratio is 1.5 (McDermid ICALP 2009, Paluch WAOA 2011, Z. Király MATCH-UP 2012), achievable by running GS on a cleverly constructed modified instance. Another elegant generalization of SM is the matroid kernel problem introduced by Fleiner (IPCO 2001), which is solvable in polynomial time using an abstract matroidal version of GS. Our main result is a simple 1.5-approximation algorithm for the matroid kernel problem with ties. We also show that the algorithm works for several other versions of stability defined for cardinal preferences, by appropriately modifying the instance on which GS is executed. The latter results are new even for the stable marriage setting.


page 1

page 2

page 3

page 4


On the approximability of the stable matching problem with ties of size two

The stable matching problem is one of the central problems of algorithmi...

An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects

The Student-Project Allocation problem with preferences over Projects (S...

A Matroid Generalization of the Super-Stable Matching Problem

A super-stable matching, which was introduced by Irving, is a solution c...

An Approximation Algorithm for Maximum Stable Matching with Ties and Constraints

We present a polynomial-time 3/2-approximation algorithm for the problem...

Host Community Respecting Refugee Housing

We propose a novel model for refugee housing respecting the preferences ...

On the Geometry of Stable Steiner Tree Instances

In this note we consider the Steiner tree problem under Bilu-Linial stab...

Stable Matchings with Flexible Quotas

We consider the problem of assigning agents to programs in the presence ...