Discussiones
Mathematicae Graph Theory 20(2) (2000) 231-242
DOI: https://doi.org/10.7151/dmgt.1122
PERSISTENCY IN THE TRAVELING SALESMAN PROBLEM ON HALIN GRAPHS
Vladimír Lacko
Department of Geometry and Algebra
P.J. Safárik University
Jesenná 5, 041 54 Košice, Slovakia
e-mail: lackov@Košice.upjs.sk
Abstract
For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency partition EAll,ESome,ENone of the edge set E, where:
EAll = {e ∈ E,e belongs to all optimum solutions},
ENone = {e ∈ E,e does not belong to any optimum solution} and
ESome = {e ∈ E,e belongs to some but not to all optimum solutions}.
Keywords: persistency, traveling salesman problem, Halin graph, polynomial algorithm.
2000 Mathematics Subject Classification: 05C45, 68Q25.
References
[1] | K. Cechlárová, Persistency in the assignment and transportation problems, Math. Methods of Operations Research 47 (1998) 234-254. |
[2] | K. Cechlárová and V. Lacko, Persistency in some combinatorial optimization problems, in: Proc. Mathematical Methods in Economy 99 (Jindrichúv Hradec, 1999) 53-60. |
[3] | K. Cechlárová and V. Lacko, Persistency in combinatorial optimization problems on matroids, to appear in Discrete Applied Math. |
[4] | G. Cornuéjols, D. Naddef and W.R. Pulleyblank, Halin graphs and the Traveling salesman problem, Mathematical Programming 26 (1983) 287-294, doi: 10.1007/BF02591867. |
[5] | M.C. Costa, Persistency in maximum cardinality bipartite matchings, Operations Research Letters 15 (1994) 143-149, doi: 10.1016/0167-6377(94)90049-3. |
[6] | V. Lacko, Persistency in optimization problems on graphs and matroids, Master Thesis, UPJS Košice, 1998. |
[7] | V. Lacko, Persistency in the matroid product problem, in: Proc. CEEPUS Modern Applied Math. Workshop (AGH Kraków, 1999), 47-51. |
Received 11 January 2000
Revised 29 March 2000
Close