On the Budgeted Priority p-Median Problem in High-Dimensional Euclidean Spaces

Given a set of clients and a set of facilities with different priority levels in a metric space, the Budgeted Priorityp-Median problem aims to open a subset of facilities and connect each client to an opened facility with the same or a higher priority level, such that the number of opened facilities associated with each priority level is no more than a given upper limit, and the sum of the client-connection costs is minimized. In this paper, we present a data reduction-based approach for limiting the solution search space of the Budgeted Priorityp-Median problem, which yields a (1+ε)-approximation algorithm running in O(ndlogn)+(pε-1)^pε-O(1)n^O(1) time in d-dimensional Euclidean space, where n is the size of the input instance and p is the maximal number of opened facilities. The previous best approximation ratio for this problem obtained in the same time is (3+ε).