Abstract
A tour cover of an edge-weighted graph is a set of edges which forms a closed walk and covers every other edge in the graph. The minimum tour cover problem is to find a minimum weight tour cover.
This problem is introduced by Arkin, Halldórsson and Hassin (Information Processing Letters 47:275-282, 1993) where the author prove the NP-hardness of the problem and give a combinatorial 5.5-approximation algorithm. Later Könemann, Konjevod, Parekh, and Sinha [7] improve the approximation factor to 3 by using a linear program of exponential size. The solution of this program involves the ellipsoid method with a separation oracle. In this paper, we present a new approximation algorithm achieving a slightly weaker approximation factor of 3.5 but only dealing with a compact linear program.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Arkin, E.M., Halldórsson, M.M., Hassin, R.: Approximating the tree and tour covers of a graph. Information Processing Letters 47, 275–282 (1993)
Carr, R., Fujito, T., Konjevod, G., Parekh, O.: A 2 1/10-approximation algorithm for a generalization of the weighted edge-dominating set problem. Journal of Combinatorial Optimization 5(3), 317–326 (2001)
Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976)
Edmonds, J., Johnson, E.L.: Matching: A Well-solved Class of Integer Linear Programs. In: Combinatorial Optimization - Eureka, You Shrink!, pp. 27–30. Springer-Verlag New York, Inc., New York (2003)
Fujito, T.: How to trim a mst: A 2-approximation algorithm for minimum cost-tree cover. ACM Trans. Algorithms 8(2), 16:1–16:11 (2012)
Fujito, T., Nagamochi, H.: A 2-approximation algorithm for the minimum weight edge dominating set problem. Discrete Applied Mathematics 118(3), 199–207 (2002)
Konemann, J., Konjevod, G., Parekh, O., Sinha, A.: Improved approximations for tour and tree covers. Algorithmica 38(3), 441–449 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Nguyen, V.H. (2014). Approximating the Minimum Tour Cover with a Compact Linear Program. In: van Do, T., Thi, H., Nguyen, N. (eds) Advanced Computational Methods for Knowledge Engineering. Advances in Intelligent Systems and Computing, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-319-06569-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-06569-4_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06568-7
Online ISBN: 978-3-319-06569-4
eBook Packages: EngineeringEngineering (R0)