Local search algorithms for the k-cardinality tree problem

Discrete Applied Mathematics

Volumn 128, Issue 2-3, 2003, Pages 511-540

  Blum, Christian ^a   Ehrgott, Matthias ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Combinatorial optimization; Genetic algorithm; k cardinality tree; Local search; Tabu search

Indexed keywords

COMBINATORIAL OPTIMIZATION; COMPUTATIONAL COMPLEXITY; FORESTRY; GENETIC ALGORITHMS; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; TABU SEARCH; TREES (MATHEMATICS);

CARDINALITIES; COMBINATORIAL OPTIMIZATION PROBLEMS; HEURISTIC SOLUTIONS; LOCAL SEARCH; LOCAL SEARCH ALGORITHM; LOCAL SEARCH METHOD; NUMERICAL RESULTS; OPTIMAL SOLUTIONS;

HEURISTIC METHODS;

EID: 84867973893     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(02)00548-6     Document Type: Article

References (40)

1. E. Aarts, and J.K. Lenstra Local Search in Combinatorial Optimization 1997 Wiley Chichester
2. S. Arora, Polynomial time approximation algorithms for Euclidean TSP and other geometric problems, in: Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, IEEE Society Press, Los Alamitos, 1996, pp. 2-11.
3. B. Awerbuch, Y. Azar, A. Blum, S. Vempala, Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen, in: Proceedings of the 27th Annual ACM Symposium on Theory of Computing, ACM Press, New York, 1995, pp. 277-283.
4. B. Awerbuch, Y. Azar, A. Blum, S. Vempala, New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen, SIAM J. Comput. 28(1) (1998) 254-262.
5. A. Blum, P. Chalasani, A. Vempala, A constant-factor approximation for the k-MST problem in the plane, in: Proceedings of the 27th Annual ACM Symposium on Theory of Computing, ACM Press, New York, 1995, pp. 294-302.
6. A. Blum, R. Ravi, A. Vempala, A constant-factor approximation for the k-MST problem, Comput. Systems Sci. 58 (1997) 101-108.
7. C. Blum, Optimality criteria and local search methods for node-weighted k-cardinality tree and subgraph problems, Master's Thesis, Department of Mathematics, University of Kaiserslautern, 1998 (in German).
8. C. Blum, M. Ehrgott, Local search algorithms for the k-cardinality tree problem, Technical Report, Department of Mathematics, University of Kaiserslautern, 1999, Report in Wirtschaftsmathematik No. 48, available at http:kluedo.ub.uni-kl.de/Mathematik/Quellen/gelb-48.pdf.
9. C. Blum, A. Roli, Metaheuristics in combinatorial optimization: overview and conceptual comparison, Technical Report, TR/IRIDIA/2001-13, IRIDIA, Université Libre de Bruxelles, 2001.
10. F. Catanas, Heuristics for the p-minimal spanning tree problem, Technical Report, Centre for Quantitative Finance, Imperial College, London, 1997.
11. S.Y. Cheung, A. Kumar, Efficient quorumcast routing algorithms, in: Proceedings of INFOCOM 94, IEEE Society Press, Los Alamitos, 1994, pp. 840-847.
12. M. Dell'Amico, A. Lodi, and F. Maffioli Solution of the cumulative assignment problem with a well-structured tabu search method J. Heuristics 5 1999 123 143
13. T. Dudas, B. Klinz, and G.J. Woeginger The computational complexity of the k-minimum spanning tree problem in graded matrices Comput. Math. Appl 36 1998 61 67
14. M. Ehrgott, Optimization problems in graphs under cardinality restrictions, Master's Thesis, Department of Mathematics, University of Kaiserslautern, 1992 (in German).
15. M. Ehrgott, J. Freitag, K-TREE / K-SUBGRAPH: a program package for minimal weighted K-cardinality-trees and -subgraphs, European J. Oper. Res. 93(1) (1996) 224-225, Code available at http://www.mathematik.uni-kl.de/~wwwwi/ WWWWI/ORSEP/contents.html.
16. M. Ehrgott, J. Freitag, H.W. Hamacher, and F. Maffioli Heuristics for the k-cardinality tree and subgraph problem Asia Pacific J. Oper. Res 14 1 1997 87 114
17. D. Eppstein Faster geometric k-point MST approximation Comput. Geom 8 5 1997 231 240
18. U. Faigle, and W. Kern Computational complexity of some maximum average weight problems with precedence constraints Oper. Res 42 4 1994 688 693
19. M. Fischetti, H.W. Hamacher, K. Joernsten, and F. Maffioli Weighted k-cardinality trees complexity and polyhedral structure Networks 24 1994 11 21
20. L.R. Foulds, H.W. Hamacher, A new integer programming approach to (restricted) facilities layout problems allowing flexible facility shapes, Technical Report 1992-1993, Department of Management Science, University of Waikato, 1992.
21. J. Freitag, Minimal k-cardinality trees, Master's Thesis, Department of Mathematics, University of Kaiserslautern, 1993 (in German).
22. N. Garg, A 3-approximation for the minimum tree spanning k vertices, in: Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, IEEE Society Press, Los Alamitos, 1996, pp. 302-309.
23. N. Garg, and D. Hochbaum An O (log k) approximation algorithm for the k minimum spanning tree problem in the plane Algorithmica 18 1997 111 121
24. F. Glover Tabu search Part I ORSA J. Comput 1 3 1989 190 206
25. F. Glover Tabu search Part II ORSA J. Comput 2 1 1990 4 32
26. H.W. Hamacher, K. Joernsten, Optimal relinquishment according to the Norwegian petrol law: a combinatorial optimization approach, Technical Report no. 7/93, Norwegian School of Economics and Business Administration, Bergen, 1993.
27. P. Hansen, The steepest ascent mildest descent heuristic for combinatorial programming, Talk presented at the Congress on Numerical Methods in Combinatorial Optimization, Capri.
28. A. Hertz, and D. Kobler A framework for the description of evolutionary algorithms European J. Oper. Res 126 2000 1 12
29. K. Joernsten, and A. Lokketangen Tabu search for weighted k-cardinality trees Asia Pacific J. Oper. Res 14 2 1997 9 26
30. F. Maffioli, Finding a best subtree of a tree, Technical Report 91.041, Politecnico di Milano, Dipartimento di Elettronica, 1991.
31. M.V. Marathe, R. Ravi, S.S. Ravi, D.J. Rosenkrantz, and R. Sundaram Spanning trees - short or small SIAM J. Discrete Math 9 2 1996 178 200
32. J.S.B. Mitchell, Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem, in: Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1996, pp. 402-408.
33. J.S.B. Mitchell Guillotine subdivisions approximate polygonal subdivisions a simple new method for the geometric k-MST problem SIAM J. Comput 28 4 1999 1298 1309
34. P. Moscato, On evolution, search, optimization, genetic algorithms and martial arts: toward memetic algorithms, Technical Report Caltech Concurrent Computation Program 826, California Institute of Technology, Pasadena, California, USA, 1989.
35. H. Mühlenbein Evolution in time and space - the parallel genetic algorithm G. Rawlins, Foundations of Genetic Algorithms 1991 Morgan-Kaufman Los Atlos, CA 316 337
36. I.H. Osman, and G. Laporte Metaheuristics a bibliography Ann. Oper. Res 63 1996 513 623
37. A.B. Philpott, N.C. Wormald, On the optimal extraction of ore from an open-cast mine, University of Auckland, New Zealand, 1997.
38. S. Rajagopalan, V.V. Vazirani, Logarithmic approximation of minimum weight k trees, unpublished manuscript, 1995.
39. G.J. Woeginger Computing maximum valued regions Acta Cybernet 10 4 1992 303 315
40. A. Zelikovsky, D. Lozevanu, Minimal and bounded trees, in: Tezele Cong. XVIII Acad. Romano-Americane, Kishinev, 1993, pp. 25-26.