Computational geometry: an introduction
Computational geometry: an introduction
Obnoxious facility location on graphs
SIAM Journal on Discrete Mathematics
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Greedily Finding a Dense Subgraph
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Finding Dense Subgraphs with Semidefinite Programming
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Facility Dispersion and Remote Subgraphs
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On the densest k-subgraph problems
On the densest k-subgraph problems
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Approximation algorithms for maximum dispersion
Operations Research Letters
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We consider geometric instances of the problem of finding a set of k vertices in a complete graph with nonnegative edge weights. In particular, we present algorithmic results for the case where vertices are represented by points in d-dimensional space, and edge weights correspond to rectilinear distances. This problem can be considered as a facility location problem, where the objective is to "disperse" a number of facilities, i.e., select a given number of locations from a discrete set of candidates, such that the average distance between selected locations is maximized. Problems of this type have been considered before, with the best result being an approximation algorithm with performance ratio 2. For the case where k is fixed, we establish a linear-time algorithm that finds an optimal solution. For the case where k is part of the input, we present a polynomial-time approximation scheme.