论文标题
通过动态编程计算核仁的一般框架
A General Framework for Computing the Nucleolus Via Dynamic Programming
论文作者
论文摘要
本文定义了一类合作游戏类别，可有效地计算核仁。该类包括新成员，以前不知道计算其核仁的复杂性。我们表明，当可以将合作游戏的最低额外联盟问题作为超图动态程序提出时，其核洛鲁斯将有效地计算。这提供了一种通用技术，用于设计有效的算法来计算合作游戏的核仁。该技术的灵感来自Pashkovich（2018）在加权投票游戏中的最新结果。但是，我们的技术大大扩展了以前工作的能力。我们通过将其应用为给出一种算法来证明这一点，以在多项式时间表上在有限的树宽图上计算B匹配游戏的核仁。
This paper defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the minimum excess coalition problem of a cooperative game can be formulated as a hypergraph dynamic program its nucleolus is efficiently computable. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich (2018) on weighted voting games. However our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidth.
