An FPTAS for Weight-Constrained Steiner Trees in Series-Parallel Graphs
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
A PTAS for weight constrained Steiner trees in series-parallel graphs
Theoretical Computer Science
Improved Approximation Algorithms for Relay Placement
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Coopetitive game, equilibrium and their applications
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Survey: A survey on relay placement with runtime and approximation guarantees
Computer Science Review
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A family of finitely many continuous functions on a polytope X, namely (g/sub i/(x))/sub i in I/, is considered, and the problem of minimizing the function f(x)=max/sub i in I/g/sub i/(x) on X is treated. It is shown that if every g/sub i/(x) is a concave function, then the minimum value of f(x) is achieved at finitely many special points in X. As an application, a long-standing problem about Steiner minimum trees and minimum spanning trees is solved. In particular, if P is a set of n points on the Euclidean plane and L/sub s/(P) and L/sub m/(P) denote the lengths of a Steiner minimum tree and a minimum spanning tree on P, respectively, it is proved that, for any P, L/sub S/(P)or= square root 3L/sub m/(P)/2, as conjectured by E.N. Gilbert and H.O. Pollak (1968).