Computing the Least-Core and Nucleolus for Threshold Cardinality Matching Games

Qizhi Fang; B. Li; Xiaoming Sun; Jia Zhang; Jialin Zhang

doi:10.1007/978-3-319-13129-0_42

Computing the Least-Core and Nucleolus for Threshold Cardinality Matching Games

Qizhi Fang, B. Li, Xiaoming Sun, Jia Zhang, Jialin Zhang

Research output: Journal article publication › Journal article › Academic research › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study the algorithmic issues on the leastcore and nucleolus of threshold cardinality matching games (TCMG). We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold T equals 1. When the threshold T is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching.

Original language	English
Pages (from-to)	474-479
Number of pages	6
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8877
DOIs	https://doi.org/10.1007/978-3-319-13129-0_42
Publication status	Published - 2014
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-319-13129-0_42

Cite this

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abstract = "In this paper, we study the algorithmic issues on the leastcore and nucleolus of threshold cardinality matching games (TCMG). We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold T equals 1. When the threshold T is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching.",

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Computing the Least-Core and Nucleolus for Threshold Cardinality Matching Games. / Fang, Qizhi; Li, B.; Sun, Xiaoming; Zhang, Jia; Zhang, Jialin.

In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 8877, 2014, p. 474-479.

Research output: Journal article publication › Journal article › Academic research › peer-review

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AU - Li, B.

AU - Sun, Xiaoming

AU - Zhang, Jia

AU - Zhang, Jialin

PY - 2014

Y1 - 2014

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AB - In this paper, we study the algorithmic issues on the leastcore and nucleolus of threshold cardinality matching games (TCMG). We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold T equals 1. When the threshold T is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching.

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Computing the Least-Core and Nucleolus for Threshold Cardinality Matching Games

Abstract

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