对象网络上的对象分配：具有严格偏好的移动代理
Object Allocation Over a Network of Objects: Mobile Agents with Strict Preferences
摘要：
在最近的研究中，Gourvès，Lesca和Wilczynski提出了经典住房市场模型的一个变体，其中代理和对象之间的匹配通过社会网络中相邻代理对之间的帕累托改进交换来演变。为了探索他们模型的交换动力学，他们提出了几个关于可达匹配集的基本问题。在他们的工作和其他后续工作中，这些问题已经针对各种类型的图进行了研究：星，路径，广义星（即，树，其中最多一个顶点的度大于2），树和团。对于广义星和树，它仍然开放是否帕累托有效的可达匹配可以找到在多项式时间。在本文中，我们追求相同的一组问题下，他们的模型的自然变体。在我们的模型中，社会网络被替换为一个对象的网络，交换是允许发生在两个代理之间，如果它是帕累托改进和相关的对象是相邻的网络。在社会网络模型的多项式时间可解性与NP难性问题已经解决的情况下，我们能够证明，同样的结果适用于对象网络模型。此外，对于我们的模型，我们提出了一个多项式时间算法计算的Pareto有效的可达匹配广义星形网络。此外，我们提出的路径网络的对象可达性算法是显着快于已知的多项式时间算法在社会网络模型中的同一问题。
英文摘要：
In recent work, Gourvès, Lesca, and Wilczynski propose a variant of the classic housing markets model where the matching between agents and objects evolves through Pareto-improving swaps between pairs of adjacent agents in a social network. To explore the swap dynamics of their model, they pose several basic questions concerning the set of reachable matchings. In their work and other follow-up works, these questions have been studied for various classes of graphs: stars, paths, generalized stars (i.e., trees where at most one vertex has degree greater than two), trees, and cliques. For generalized stars and trees, it remains open whether a Pareto-efficient reachable matching can be found in polynomial time. In this paper, we pursue the same set of questions under a natural variant of their model. In our model, the social network is replaced by a network of objects, and a swap is allowed to take place between two agents if it is Pareto-improving and the associated objects are adjacent in the network. In those cases where the question of polynomial-time solvability versus NP-hardness has been resolved for the social network model, we are able to show that the same result holds for the network-of-objects model. In addition, for our model, we present a polynomial-time algorithm for computing a Pareto-efficient reachable matching in generalized star networks. Moreover, the object reachability algorithm that we present for path networks is significantly faster than the known polynomial-time algorithms for the same question in the social network model.
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