Parameterized algorithms for stable matching with ties and incomplete lists

Deeksha Adil; Sushmita Gupta; Sanjukta Roy; Saket Saurabh; Meirav Zehavi

doi:10.1016/j.tcs.2018.03.015

Parameterized algorithms for stable matching with ties and incomplete lists

Deeksha Adil, Sushmita Gupta, Sanjukta Roy, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We study the parameterized complexity of NP-hard optimization versions of STABLE MATCHING and STABLE ROOMMATES in the presence of ties and incomplete lists. These problems model many real-life situations where solutions have to satisfy certain predefined criterion of suitability and compatibility. Specifically, our objective is to maximize/minimize the size of the stable matching. Our main theorems state that STABLE MATCHING and STABLE ROOMMATES admit small kernels. Consequently, we also conclude that STABLE MATCHING is fixed-parameter tractable (FPT) with respect to solution size, and that STABLE ROOMMATES is FPT with respect to a structural parameter. Finally, we analyze the special case where the input graph is planar.

Original language	American English
Pages (from-to)	1-10
Number of pages	10
Journal	Theoretical Computer Science
Volume	723
DOIs	https://doi.org/10.1016/j.tcs.2018.03.015
State	Published - 2 May 2018

Keywords

Parameterized complexity
Preference list
Stable matching

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2018.03.015

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title = "Parameterized algorithms for stable matching with ties and incomplete lists",

abstract = "We study the parameterized complexity of NP-hard optimization versions of STABLE MATCHING and STABLE ROOMMATES in the presence of ties and incomplete lists. These problems model many real-life situations where solutions have to satisfy certain predefined criterion of suitability and compatibility. Specifically, our objective is to maximize/minimize the size of the stable matching. Our main theorems state that STABLE MATCHING and STABLE ROOMMATES admit small kernels. Consequently, we also conclude that STABLE MATCHING is fixed-parameter tractable (FPT) with respect to solution size, and that STABLE ROOMMATES is FPT with respect to a structural parameter. Finally, we analyze the special case where the input graph is planar.",

keywords = "Parameterized complexity, Preference list, Stable matching",

author = "Deeksha Adil and Sushmita Gupta and Sanjukta Roy and Saket Saurabh and Meirav Zehavi",

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T1 - Parameterized algorithms for stable matching with ties and incomplete lists

AU - Adil, Deeksha

AU - Gupta, Sushmita

AU - Roy, Sanjukta

AU - Saurabh, Saket

AU - Zehavi, Meirav

PY - 2018/5/2

Y1 - 2018/5/2

N2 - We study the parameterized complexity of NP-hard optimization versions of STABLE MATCHING and STABLE ROOMMATES in the presence of ties and incomplete lists. These problems model many real-life situations where solutions have to satisfy certain predefined criterion of suitability and compatibility. Specifically, our objective is to maximize/minimize the size of the stable matching. Our main theorems state that STABLE MATCHING and STABLE ROOMMATES admit small kernels. Consequently, we also conclude that STABLE MATCHING is fixed-parameter tractable (FPT) with respect to solution size, and that STABLE ROOMMATES is FPT with respect to a structural parameter. Finally, we analyze the special case where the input graph is planar.

AB - We study the parameterized complexity of NP-hard optimization versions of STABLE MATCHING and STABLE ROOMMATES in the presence of ties and incomplete lists. These problems model many real-life situations where solutions have to satisfy certain predefined criterion of suitability and compatibility. Specifically, our objective is to maximize/minimize the size of the stable matching. Our main theorems state that STABLE MATCHING and STABLE ROOMMATES admit small kernels. Consequently, we also conclude that STABLE MATCHING is fixed-parameter tractable (FPT) with respect to solution size, and that STABLE ROOMMATES is FPT with respect to a structural parameter. Finally, we analyze the special case where the input graph is planar.

KW - Parameterized complexity

KW - Preference list

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JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Parameterized algorithms for stable matching with ties and incomplete lists

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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