Symmetric range assignment with disjoint MST constraints

If V is a set of n points in the unit square [0, 1]2 , and if R : V + is an assignment of positive real numbers (radii) to to those points, define a graph G(R) as follows: {v, w} is an undirected edge if and only if the Euclidean distance d(v, w) is less than or equal to min(R(v), R(w)). Given 1 and k Z+, let R k be the range assignment that minimizes the function J(R) = P vV R(v) , subject to the constraint that G(R) has at least k edge-disjoint spanning trees. For n random points in [0, 1]2 , the expected value of the optimum, E(J(R k)), is asymptotically (n12 ). This is proved by analyzing a crude approximation algorithm that finds a range assignment Ra k such that the ratio J(Ra k) J(R k ) is bounded. Categories and Subject Descriptors F.2.m [Analysis of Algorithms and Problem Complexity]: Miscellaneous General Terms Algorithms, Performance, Reliability, Theory Keywords Range assignment, probabilistic analysis, approximation algorithm, spanning tree

• Type: Conference
• Year: 2008
• Where: DIALM
• Authors: Eric Schmutz
• Keywords: Algorithms, Approximation Algorithm, DIALM 2008, Range Assignment, Spanning Tree