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From Balls and Bins to Points and Vertices

  • Ralf Klasing
  • Zvi Lotker
  • Alfredo Navarra
  • Stephane Perennes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)

Abstract

Given a graph G=(V,E) with |V|=n, we consider the following problem. Place n points on the vertices of G independently and uniformly at random. Once the points are placed, relocate them using a bijection from the points to the vertices that minimizes the maximum distance between the random place of the points and their target vertices.

We look for an upper bound on this maximum relocation distance that holds with high probability (over the initial placements of the points).

For general graphs, we prove the #P-hardness of the problem and that the maximum relocation distance is \(O(\sqrt{n})\) with high probability. We also present a Fully Polynomial Randomized Approximation Scheme when the input graph admits a polynomial-size family of witness cuts while for trees we provide a 2-approximation algorithm.

Keywords

Polynomial Time Greedy Algorithm Random Point Token Distribution Clique Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ralf Klasing
    • 1
  • Zvi Lotker
    • 2
  • Alfredo Navarra
    • 3
  • Stephane Perennes
    • 4
  1. 1.LaBRIUniversité Bordeaux 1Talence cedexFrance
  2. 2.Centrum voor Wiskunde en InformaticaAmsterdamNetherlands
  3. 3.Computer Science DepartmentUniversity of L’AquilaItaly
  4. 4.MASCOTTE projectI3S-CNRS/INRIA/Univ. Nice–Sophia AntipolisFrance

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