STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES

Maria Silvia Pini, Francesca Rossi, Kristen Brent Venable, Toby Walsh

2011

Abstract

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with weighted preferences: each man (resp., woman) provides a score for each woman (resp., man). Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations it is more natural to express scores (to model, for example, profits or costs) rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages which are stable and/or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

Paper Citation

in Harvard Style

Pini M., Rossi F., Venable K. and Walsh T. (2011). STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES . In Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8425-41-6, pages 45-53. DOI: 10.5220/0003144200450053

in Bibtex Style

@conference{icaart11,
author={Maria Silvia Pini and Francesca Rossi and Kristen Brent Venable and Toby Walsh},
title={STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES},
booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2011},
pages={45-53},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003144200450053},
isbn={978-989-8425-41-6},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES
SN - 978-989-8425-41-6
AU - Pini M.
AU - Rossi F.
AU - Venable K.
AU - Walsh T.
PY - 2011
SP - 45
EP - 53
DO - 10.5220/0003144200450053