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The Maximum Exposure Problem

Authors Neeraj Kumar, Stavros Sintos, Subhash Suri

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • max-exposure
  • PTAS
  • densest k-subgraphs
  • geometric constraint removal
  • Network resilience

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Abstract

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.

Cite As Get BibTex

Neeraj Kumar, Stavros Sintos, and Subhash Suri. The Maximum Exposure Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.19

Author Details

Neeraj Kumar
  • Department of Computer Science, University of California, Santa Barbara, USA
Stavros Sintos
  • Duke University, Durham, NC, USA
Subhash Suri
  • Department of Computer Science, University of California, Santa Barbara, USA

Funding

Work by Kumar and Suri is supported by NSF under Grant CCF-1814172. Work by Sintos is supported by NSF under grants CCF-15-13816, CCF-15-46392, and IIS-14-08846, by ARO grant W911NF-15-1-0408, and by Grant 2012/229 from the U.S.-Israel Binational Science Foundation.

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