Strategic clustering

How much does the quality of the clustering — typically measured by the conductance, or by the number of edges cut, or the average distance to the centers — deteriorate if the nodes are strategic and can change clusters? And among reasonable utilities for the nodes, which one hurts quality the least? We investigate these questions both theoretically, by studying the equilibria of hedonic games (simplified clustering games with unconstrained number of clusters), and experimentally, by measuring the quality of pure Nash equilibria of more realistic clustering games. We introduce a new utility function for the nodes which we call closeness , and which we believe is an attractive alternative to previously studied node utilities. We study the properties of the closeness utility theoretically and demonstrate experimentally its advantages over other established utilities such as the modified fractional utility. Finally, we present a polynomial-time algorithm which, given a clustering with optimal quality, finds another clustering with better average utility, and in fact the one that maximizes the ratio of the gain in average utility over the loss in quality.

聚类的质量通常是通过电导率或削减的边缘数量或与中心的平均距离来衡量的，这些节点是否是战略性的，可以更改簇？哪一个谋杀质量最少？纯净的NASH质量相当于更现实的聚类游戏。在实验中，它的优势比其他建立的实用程序，例如修改的分数效用。最佳质量，找到了另一个具有更好平均效用的聚类，实际上，它是最大化平均效用比质量损失的比率的比率。