eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-17
19:1
19:20
10.4230/LIPIcs.APPROX-RANDOM.2019.19
article
The Maximum Exposure Problem
Kumar, Neeraj
1
Sintos, Stavros
2
Suri, Subhash
1
Department of Computer Science, University of California, Santa Barbara, USA
Duke University, Durham, NC, USA
Given a set of points P and axis-aligned rectangles R in the plane, a point p in P is called exposed if it lies outside all rectangles in R. In the max-exposure problem, given an integer parameter k, we want to delete k rectangles from R so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in R are translates of two fixed rectangles. However, if R only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For general rectangle range space, we present a simple O(k) bicriteria approximation algorithm; that is by deleting O(k^2) rectangles, we can expose at least Omega(1/k) of the optimal number of points.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol145-approx-random2019/LIPIcs.APPROX-RANDOM.2019.19/LIPIcs.APPROX-RANDOM.2019.19.pdf
max-exposure
PTAS
densest k-subgraphs
geometric constraint removal
Network resilience