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Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem
Open accessAbstract
An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cost perfect matching of a certain induced subgraph of G. A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial growth algorithms for the TSP.
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Cited by
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Williamson, D. P., & Shmoys, D. B. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511921735 · Cited by 1,301
The General Pickup and Delivery Problem
Savelsbergh, M. W. P., & Sol, M. (1995) · Transportation Science · doi:10.1287/trsc.29.1.17 · Cited by 1,042
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Hadfield, S., Wang, Z., O’Gorman, B., Rieffel, E. G., Venturelli, D., & Biswas, R. (2019) · Algorithms · doi:10.3390/a12020034 · Cited by 772
Robotic kiwifruit harvesting using machine vision, convolutional neural networks, and robotic arms
Williams, H. A. M., Jones, M. H., Nejati, M., Seabright, M. J., Bell, J., Penhall, N. D., Barnett, J. J., Duke, M. D., Scarfe, A. J., Ahn, H. S., et al. (2019) · Biosystems Engineering · doi:10.1016/j.biosystemseng.2019.03.007 · Cited by 346
Metadata
- Authors
- Christofides, N.
- Venue
- Operations Research Forum
- Published
- 2022-03
- Volume
- 3
- Issue
- 1
- ISSN
- 2662-2556 (ISSN-L)
- OpenAlex
- W2117226423
- Cited by
- 1,131
- References
- 0
- FWCI
- 23.31
- Type
- journal article
- Language
- en
- Open access
- hybrid
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