An Improved FPT Approximation Algorithm for Diversity-Aware L-Centrum

We propose and study the diversity-aware l-centrum (div-l-centrum) problem, where we are given a set of clients and a set of facilities in a metric space, integers k and l, and r[i] (i∈[t]) for each facility group. The diversity constraints refer to the requirement that each group must include at least r[i] open facilities. The goal is to find a subset of facilities of size at most k so as to minimize the sum of the l largest distances from a client to its nearest open facility, while satisfying the diversity constraints. As our main contribution, we provide a fixed-parameter tractable (1+2/e+ε)-approximation algorithm that improves upon the previous (3+ε) for the div-l-centrum problem, based on a combination of leader selection, coreset construction and submodular optimization techniques.