Abstract
AbstractWe show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than$$-$$
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1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, combined with a novel use of max-entropy sampling, can give better guarantees.
Funder
Carnegie Mellon University
Publisher
Springer Science and Business Media LLC
Reference16 articles.
1. Asadpour, A., Goemans, M.X., Mźdry, A., Oveis Gharan, S., Saberi, A.: An o(log n/log log n)-approximation algorithm for the asymmetric traveling salesman problem. Oper. Res. 65(4), 1043–1061 (2017)
2. Borcea, J., Brändéd, P., Liggett, T.M.: Negative dependence and the geometry of polynomials. J. Am. Math. Soc. 22(2), 521–567 (2009)
3. Boyd, S., Sebő, A.: The salesman’s improved tours for fundamental classes. Math. Program. 186(1–2), 289–307 (2021)
4. Christofides, Nicos: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report 338, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA, (1976)
5. Chekuri, C, Vondrak, J, Zenklusen, R: Dependent randomized rounding via exchange properties of combinatorial structures. In 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pp 575–584, (2010)