On the solution value of the continuous P-center location problem on a graph
Mathematics of Operations Research
Improved complexity bounds for center location problems on networks by using dynamic data structures
SIAM Journal on Discrete Mathematics
New upper bounds in Klee's measure problem
SIAM Journal on Computing
On some optimization problems on k-trees and partial k-trees
Discrete Applied Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Introduction to algorithms
Efficient algorithms for center problems in cactus networks
Theoretical Computer Science
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
Algorithms for graphs of bounded treewidth via orthogonal range searching
Computational Geometry: Theory and Applications
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In this paper we show that a p(=2)-center location problem in general networks can be transformed to the well-known Klee@?s measure problem (Overmars and Yap, 1991) [15]. This results in a significantly improved algorithm for the continuous case with running time O(m^pn^p^/^22^l^o^g^^^@?^nlogn) for p=3, where n is the number of vertices, m is the number of edges, and log^@?n denotes the iterated logarithm of n (Cormen et al., 2001) [10]. For p=2, the running time of the improved algorithm is O(m^2nlog^2n). The previous best result for the problem is O(m^pn^p@a(n)logn) where @a(n) is the inverse Ackermann function (Tamir, 1988) [17]. When the underlying network is a partial k-tree (k fixed), we exploit the geometry inherent in the problem and propose a two-level tree decomposition data structure which can be used to efficiently solve discrete p-center problems for small values of p.