On the exact solution of the Euclidean three-matching problem

Magyar Gábor and Johnsson Mika and Nevalainen Olli: On the exact solution of the Euclidean three-matching problem. In: Acta cybernetica, (14) 2. pp. 357-366. (1999)

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Three-Matching Problem (3MP) is an NP-complete graph problem which has applications in the field of inserting electronic components on a printed circuit board. In 3MP we want to partition a set of n = 31 points into I disjoint subsets, each containing three points (triplets) so that the total cost of the triplets is minimal. We consider the problem where the cost Cijk of a triplet is the sum of the lengths of the two shortest edges of the triangle (i, j, k)\ the reason for this assumption is the nature of the practical problems. In this paper we discuss the optimal solution of 3MP. W e give two different integer formulations and several lower bounds of the problem based on the Lagrangian relaxations of the integer programs. The different lower bounds are evaluated by empirical comparisons. We construct branch-andbound procedures for solving 3MP by completing the best lower bound with appropriate branching operations. The resulting procedures are compared to our previous exact method and to general MIP solvers.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 1999
Volume: 14
Number: 2
ISSN: 0324-721X
Page Range: pp. 357-366
Language: English
Place of Publication: Szeged
Event Title: Conference for PhD Students in Computer Science (1.) (1998) (Szeged)
Related URLs: http://acta.bibl.u-szeged.hu/38508/
Uncontrolled Keywords: Számítástechnika, Kibernetika, Algoritmus
Additional Information: Bibliogr.: p. 375-376. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2016. Oct. 15. 12:26
Last Modified: 2022. Jun. 14. 09:46
URI: http://acta.bibl.u-szeged.hu/id/eprint/12632

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