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SIAM Journal on Computing
An O(n) algorithm for the linear multiple choice knapsack problem and related problems
Information Processing Letters
A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
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Journal of the ACM (JACM)
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
A heuristic for the p-center problem in graphs
Discrete Applied Mathematics
Improved complexity bounds for center location problems on networks by using dynamic data structures
SIAM Journal on Discrete Mathematics
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
New upper bounds in Klee's measure problem
SIAM Journal on Computing
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Applications of parametric searching in geometric optimization
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Fault tolerant K-center problems
Theoretical Computer Science
Polynomially Solvable Cases of the Simple Plant Location Problem
Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference
Improvements on Geometric Pattern Matching Problems
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Single facility collection depots location problem in the plane
Computational Geometry: Theory and Applications
On the round-trip 1-center and 1-median problems
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
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In the classical p-center problem there is a set V of points (customers) in some metric space, and the objective is to locate p centers (servers), minimizing the maximum distance between a customer and his respective nearest server. In this paper we consider an extension, where each customer is associated with a set of existing depots or distribution stations he can use. The service of a customer consists of the travel of a server to some permissible depot, loading of some package (e.g., a spare part) at the depot, and the delivery of the package to the customer. This model is called the customer one-way problem. In the round-trip version of the problem, the service also includes the travel from the customer to the home base of the server. In both problems the customer cost of the service is a linear function of the distance travelled by the server. The objective is to locate p servers, minimizing the maximum customer cost (weighted distance travelled by the respective server). Since the classical p-center problem is NP-hard, so are the one-way and the round-trip models we study. We present efficient constant factor approximation algorithms for these problems on general networks. Turning to special networks, we prove that the one-way problem is strongly NP-hard even on path networks. We then present polynomial time algorithms for the round-trip problem on general tree networks. We also discuss the single center case, and provide polynomial time algorithms for general networks, tree networks and planar Euclidean and rectilinear metric spaces.