Polynomial-time approximation schemes for piercing and covering with applications in wireless networks

  • Authors:

  • Paz Carmi;Matthew J. Katz;Nissan Lev-Tov

  • Affiliations:

  • Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2008

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Abstract

Let D be a set of disks of arbitrary radii in the plane, and let P be a set of points. We study the following three problems: (i) Assuming P contains the set of center points of disks in D, find a minimum-cardinality subset P^* of P (if exists), such that each disk in D is pierced by at least h points of P^*, where h is a given constant. We call this problem minimum h-piercing. (ii) Assuming P is such that for each D@?D there exists a point in P whose distance from D's center is at most @ar(D), where r(D) is D's radius and 0=