| P. Carraresi and C. Sodini. A binary enumeration tree to find K shortest paths. Proc. 7th Symp. Operations Research, pp. 177--188. Athen aum/Hain/Hanstein, Methods of Operations Research 45, 1983. |
....term above can be omitted. The related problem of finding the k longest paths in a DAG [4] can be transformed to a shortest path problem simply by negating all edge lengths; we can therefore also solve it in the same time bounds. 1. 3 Related Work Many papers study algorithms for k shortest paths [3, 5,7,9,13,14,17,24,31,32,34,35,37 41,43 45, 47, 50, 51, 56 60, 63, 65 69]. Dreyfus [17] and Yen [69] cite several additional papers on the subject going back as far as 1957. One must distinguish several common variations of the problem. In many of the papers cited above, the paths are restricted to be simple, i.e. no vertex can be repeated. This has advantages in some ....
P. Carraresi and C. Sodini. A binary enumeration tree to find K shortest paths. Proc. 7th Symp. Operations Research, pp. 177--188. Athen aum/Hain/Hanstein, Methods of Operations Research 45, 1983.
....the time bounds above should be modified to include the time to compute a single source shortest path tree in such networks. Similar results also hold for finding the k longest paths in acyclic networks [4] we omit the details. 1. 3 Related Work The k shortest paths problem has been well studied [3, 5, 7, 9, 12, 17, 18, 20, 21, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42] and many algorithms are known. Dreyfus [9] and Yen [42] cite several additional papers on the subject going back as far as 1957. One must distinguish several common variations of the problem. In many of the papers cited above, the paths are restricted to be simple, i.e. no vertex can be ....
P. Carraresi and C. Sodini. A binary enumeration tree to find k shortest paths. In 7th Symp. Operations Research, pages 177--188. Methods of Operations Research, 1983.
.... With algorithms available from so many different branches of mathematics, it is difficult to compare them all without implementing them and as such, the following papers present alternative techniques from other fields that may yet perform faster than Hoffman s algorithm: Shier [8] Carraresi [9], and Boffey [10] However, these do not all meet the restrictions of loopless and nondisjoint paths, so extra precautions will have to be taken. 10 Acknowledgements The research that is described in this paper was undertaken by the first author (supervised by the second) as part of an M.Sc. in ....
Carraresi P, Sodini C. A binary enumeration tree to find k shortest paths. Methods of Operations Research (Germany) 7th Symposium on Operations Research, St. Gallen, Switzerland 1983; 177--188
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