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Title: Submodular Clustering in Low Dimensions
We study a clustering problem where the goal is to maximize the coverage of the input points by k chosen centers. Specifically, given a set of n points P ⊆ ℝ^d, the goal is to pick k centers C ⊆ ℝ^d that maximize the service ∑_{p∈P}φ(𝖽(p,C)) to the points P, where 𝖽(p,C) is the distance of p to its nearest center in C, and φ is a non-increasing service function φ: ℝ+ → ℝ+. This includes problems of placing k base stations as to maximize the total bandwidth to the clients - indeed, the closer the client is to its nearest base station, the more data it can send/receive, and the target is to place k base stations so that the total bandwidth is maximized. We provide an n^{ε^-O(d)} time algorithm for this problem that achieves a (1-ε)-approximation. Notably, the runtime does not depend on the parameter k and it works for an arbitrary non-increasing service function φ: ℝ+ → ℝ+.  more » « less
Award ID(s):
1907400
PAR ID:
10226328
Author(s) / Creator(s):
;
Date Published:
Journal Name:
17th Scandinavian Symposium and Workshops on Algorithm Theory
Volume:
162
Page Range / eLocation ID:
8:1--8:14
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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