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+.
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Microwave resonance in a high-quality GaAs/AlGaAs two-dimensional electron system in the low-density and low-mobility condition
- Award ID(s):
- 1710302
- NSF-PAR ID:
- 10120424
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 100
- Issue:
- 15
- ISSN:
- 2469-9950; PRBMDO
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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