Kavitha, Telikepalli and Nasre, Meghana
(2009)
*Popular Matchings with Variable Job Capacities.*
In: 20th International Symposium on Algorithms and Computations (ISAAC 2009), DEC 16-18, 2009, Honolulu, pp. 423-433.

## Abstract

We consider the problem of matching people to jobs, where each person ranks a subset of jobs in an order of preference, possibly involving ties. There are several notions of optimality about how to best match each person to a job; in particular, popularity is a natural and appealing notion of optimality. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not adroit popular matchings. This motivates the following extension of the popular rnatchings problem:Given a graph G; = (A boolean OR J, E) where A is the set of people and J is the set of jobs, and a list < c(1), c(vertical bar J vertical bar)) denoting upper bounds on the capacities of each job, does there exist (x(1), ... , x(vertical bar J vertical bar)) such that setting the capacity of i-th, job to x(i) where 1 <= x(i) <= c(i), for each i, enables the resulting graph to admit a popular matching. In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c is 1 or 2.

Item Type: | Conference Paper |
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Series.: | Lecture Notes in Computer Science |

Publisher: | Springer |

Additional Information: | Copyright of this article belongs to Springer. |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 25 Aug 2010 05:05 |

Last Modified: | 26 Oct 2018 14:44 |

URI: | http://eprints.iisc.ac.in/id/eprint/31342 |

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