Persistency in the Traveling Salesman Problem on Halin graphs

• Autorzy: Vladimír Lacko
• Języki publikacji: EN

Abstrakty

EN

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 $E_{All}$, $E_{Some}$, $E_{None}$ of the edge set E, where:
$E_{All}$ = {e ∈ E, e belongs to all optimum solutions},
$E_{None}$ = {e ∈ E, e does not belong to any optimum solution} and
$E_{Some}$ = {e ∈ E, e belongs to some but not to all optimum solutions}.

Słowa kluczowe

EN

persistency; traveling salesman problem; Halin graph; polynomial algorithm

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 68Q25: Analysis of algorithms and problem complexity

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 231-242

Daty

wydano

2000

otrzymano

2000-01-11

poprawiono

2000-03-29

Twórcy

autor

Vladimír Lacko

• Department of Geometry and Algebra, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1122