1. BEATING THE INTEGRALITY RATIO FOR s-t-TOURS IN GRAPHS.
- Author
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TRAUB, VERA and VYGEN, JENS
- Subjects
- *
TRAVELING salesman problem , *APPROXIMATION algorithms , *GRAPH algorithms - Abstract
Among various variants of the traveling salesman problem (TSP), the s-t-path graph TSP has the special feature that we know the exact integrality ratio, 3 2, and an approximation algorithm matching this ratio. In this paper, we go below this threshold: we devise a polynomialtime algorithm for the s-t-path graph TSP with approximation ratio 1.497. Our algorithm can be viewed as a refinement of the 3 2 -approximation algorithm in [A. SebH o and J. Vygen, Combinatorica, 34 (2014), pp. 597--629], but we introduce several completely new techniques. These include a new type of ear-decomposition, an enhanced ear induction that reveals a novel connection to matroid union, a stronger lower bound, and a reduction of general instances to instances in which s and t have small distance (which works for general metrics). [ABSTRACT FROM AUTHOR]
- Published
- 2023
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