TY - GEN

T1 - From balls and bins to points and vertices

AU - Klasing, Ralf

AU - Lotker, Zvi

AU - Navarra, Alfrede

AU - Perennes, Stephane

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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(√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.

AB - 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(√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.

UR - http://www.scopus.com/inward/record.url?scp=33744951537&partnerID=8YFLogxK

U2 - 10.1007/11602613_76

DO - 10.1007/11602613_76

M3 - Conference contribution

AN - SCOPUS:33744951537

SN - 3540309357

SN - 9783540309352

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 757

EP - 766

BT - Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings

T2 - 16th International Symposium on Algorithms and Computation, ISAAC 2005

Y2 - 19 December 2005 through 21 December 2005

ER -