Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 1: 47 - 63

DOI: https://doi.org/10.1007/s11464-009-0048-y

Research articles

Algorithms for core stability, core largeness, exactness, and extendability of flow games

Expand
  • 1.Department of Mathematics, Ocean University of China, Qingdao 266100, China; 2.Department of Computer Science and Engineering, Fudan University, Shanghai 200433, China; 3.Department of Computer Science, University of Maryland, College Park, MD 20742, USA; 4.Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350, Australia;

Published date: 05 Mar 2010

Fold

Abstract

We study core stability and some related properties of flow games defined on simple networks (all edge capacities are equal) from an algorithmic point of view. We first present a sufficient and necessary condition that can be tested efficiently for a simple flow game to have a stable core. We also prove the equivalence of the properties of core largeness, extendability, and exactness of simple flow games and provide an equivalent graph theoretic characterization which allows us to decide these properties in polynomial time.

Key words： Flow network; series-parallel graph; imputation; cooperative game

Cite this article

Qizhi FANG, Rudolf FLEISCHER, Jian LI, Xiaoxun SUN, . Algorithms for core stability, core largeness, exactness, and extendability of flow games[J]. Frontiers of Mathematics in China, 2010 , 5(1) : 47 -63 . DOI: 10.1007/s11464-009-0048-y

Options
Outlines

/

〈 〉