Best network flow bounds for the quadratic knapsack problem
COMO '86 Lectures given at the third session of the Centro Internazionale Matematico Estivo (C.I.M.E.) on Combinatorial optimization
Good solutions to discrete noxious location problems via metaheuristics
Annals of Operations Research - Special issue on locational decisions
A lower bound for a constrained quadratic 0-1 minimization problem
Discrete Applied Mathematics
Complexity of finding dense subgraphs
Discrete Applied Mathematics
Quadratic Knapsack Relaxations Using Cutting Planes
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
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
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
Discrete location problems with push-pull objectives
Discrete Applied Mathematics
Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction
INFORMS Journal on Computing
Approximation algorithms for maximum dispersion
Operations Research Letters
A general heuristic for vehicle routing problems
Computers and Operations Research
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The p-dispersion-sum problem is the problem of locating p facilities at some of n predefined locations, such that the distance sum between the p facilities is maximized. The problem has applications in telecommunication (where it is desirable to disperse the transceivers in order to minimize interference problems), and in location of shops and service-stations (where the mutual competition should be minimized).A number of fast upper bounds are presented based on Lagrangian relaxation, semidefinite programming and reformulation techniques. A branch-and-bound algorithm is then derived, which at each branching node is able to compute the reformulation-based upper bound in O(n) time. Computational experiments show that the algorithm may solve geometric problems of size up to n = 90, and weighted geometric problems of size n = 250.The related p-dispersion problem is the problem of locating p facilities such that the minimum distance between two facilities is as large as possible. New formulations and fast upper bounds are presented, and it is discussed whether a similar framework as for the p-dispersion sum problem can be used to tighten the upper bounds. A solution algorithm based on transformation of the p-dispersion problem to the p-dispersion-sum problem is finally presented, and its performance is evaluated through several computational experiments.