Abstract
In this paper we describe a computational study to solve hard frequency assignment problems (FAPs) to optimality using a tree decomposition of the graph that models interference constraints. We present a dynamic programming algorithm which solves FAPs based on this tree decomposition. With the use of several dominance and bounding techniques it is possible to solve small and medium-sized real-life instances of the frequency assignment problem to optimality. Moreover, with an iterative version of the algorithm we obtain good lower bounds for large-sized instances within reasonable time and memory limits.
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References
S. Arnborg, D.G. Corneil, and A. Proskurowski. Complexity of finding embeddins in a k-tree. SIAM Journal on Algebraic and Discrete Methods, 8:277–284, 1987. 341
H.L. Bodlaender. A tourist guide through treewidth. Acta Cybernetica, 11(1-2):1–21, 1993. 339
H.L. Bodlaender. “A linear time algorithm for finding tree-decompositions of small treewidth”. SIAM Journal on Computing, 25(6):1305–1317, 1996. 341
D.J. Castelino, S. Hurley, and N.M. Stephens. A tabu search algorithm for frequency assignment. Annals of Operations Research, 63:301–319, 1996. 339
A. Kolen. A genetic algorithm for frequency assignment. Technical report, Maastricht University, 1999. Available at http://www.unimaas.nl/~akolen/. 339, 347
A.M.C.A. Koster, C.P.M. van Hoesel, and A.W.J. Kolen. The partial constraint satisfaction problem: Facets and lifting theorems. Operations Research Letters, 23(3-5):89–97, 1998. 339, 341
A.M.C.A. Koster, C.P.M. van Hoesel, and A.W.J. Kolen. Solving frequency assignment problems via tree-decomposition. Technical Report RM 99/011, Maastricht University, 1999. Available at http://www.unimaas.nl/~akoster/. 340, 341, 343, 346
N. Robertson and P.D. Seymour. Graph minors. II. algorithmic aspects of treewidth. Journal of Algorithms, 7:309–322, 1986. 339, 341
S. Tiourine, C. Hurkens, and J.K. Lenstra. “An overview of algorithmic approaches to frequency assignment problems”. In Calma Symposium on Combinatorial Algorithms for Military Applications, pages 53–62, 1995. Available at http://www.win.tue.nl/math/bs/combopt/hurkens/calma.html. 339
S. R. Tiourine, C.A.J. Hurkens, and J.K. Lenstra. Local search algorithms for the radio link frequency assignment problem. Telecommunication systems, to appear, 1999. 339, 339
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© 1999 Springer-Verlag Berlin Heidelberg
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Koster, A.M.C.A., van Hoesel, S.P., Kolen, A.W. (1999). Optimal Solutions for Frequency Assignment Problems via Tree Decomposition. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_32
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DOI: https://doi.org/10.1007/3-540-46784-X_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66731-5
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