eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-12
8:1
8:14
10.4230/LIPIcs.SWAT.2020.8
article
Submodular Clustering in Low Dimensions
Backurs, Arturs
1
Har-Peled, Sariel
2
Toyota Technological Institute at Chicago, Il, USA
University of Illinois at Urbana-Champaign, Il, USA
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+.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol162-swat2020/LIPIcs.SWAT.2020.8/LIPIcs.SWAT.2020.8.pdf
clustering
covering
PTAS