Journal of Algorithms
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Algorithms for clustering data
Algorithms for clustering data
An algorithm for the three-index assignment problem
Operations Research
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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In the 3-matching problem (3MP) we want to partition a set of n = 3l points into l disjoint subsets, each consisting of three points (called triplets), and to minimize the total cost of the triplets. The problem is related to the well-known weighted 2-matching, 3-dimensional assignment and p-median problems. We consider a Euclidean 3MP (E3MP) where the cost cijk of a triplet (i, j, k) is the sum of the lengths of the two shortest edges of the triangle (i, j, k). The problem has several related applications in the optimization of manufacturing operations.We show that the general 3MP is NP-complete and give several methods to calculate lower bounds for the E3MP. The exact solution by branch-and-bound technique is possible for small instances. For large problem instances we have to apply approximative solution algorithms. Local search-based heuristics augmented with ideas from tabu-search, simulated annealing and genetic algorithms worked well in our tests.