Exact capacitated domination：关于唯一性的计算复杂性
Exact capacitated domination: on the computational complexity of uniqueness
摘要：
在本文中，我们考虑了一个本地的服务需求分配问题命名为精确的能力控制从算法的角度来看。这个问题的目的是找到一个解决方案（纳什均衡）的博弈论模型的公共品提供。在这个问题中，我们给出了一个有能力的图，一个在每个顶点上定义了一个参数的图，这个参数被解释为该顶点的能力。我们的目标是找到一个DP-Nash子图：一个生成二部子图，它的二部集合D和P分别称为D-集合和P-集合，使得P中没有孤立的顶点，并且D中的每个顶点都与等于其容量的顶点相邻。我们证明了一个有容量限制的图是否有唯一的DP-Nash子图可以在多项式时间内确定。然而，我们也表明，附近的问题，决定是否有一个唯一的D-集的容量限制图是co-NP-完全的。
英文摘要：
In this paper we consider a local service-requirement assignment problem named exact capacitated domination from an algorithmic point of view. This problem aims to find a solution (a Nash equilibrium) to a game-theoretic model of public good provision. In the problem we are given a capacitated graph, a graph with a parameter defined on each vertex that is interpreted as the capacity of that vertex. The objective is to find a DP-Nash subgraph: a spanning bipartite subgraph with partite sets D and P, called the D-set and P-set respectively, such that no vertex in P is isolated and that each vertex in D is adjacent to a number of vertices equal to its capacity. We show that whether a capacitated graph has a unique DP-Nash subgraph can be decided in polynomial time. However, we also show that the nearby problem of deciding whether a capacitated graph has a unique D-set is co-NP-complete.
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