In the aversion k-clustering problem, given a metric space, we want to cluster the points into k clusters. The cost incurred by each point is the distance to the furthest point in its cluster, and the cost of the clustering is the sum of all these per-point-costs. This problem is motivated by questions in generating automatic abstractions of extensive-form games.
We reduce this problem to a local k-median problem where each facility has a prescribed radius and can only connect to clients within that radius. Our main results is a constant-factor approximation algorithm for the aversion k-clustering problem. We use a primal-dual approach; our technical contribution is a non-local rounding step which we feel is of broader interest.
Presented in Partial Fulfillment of the CSD Speaking Skills Requirement.
BIO:
Guru Guruganesh is a PhD student at Carnegie Mellon University advised by Anupam Gupta. His research interests include approximation algorithms, network design and online algorithms.