D. R. Shier: "Iterative Methods for Determining the k Shortest Paths in a Network", Networks, vol. 6, pp. 205--229. (1976)  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... log d) where d is the maximum input degree [Fox73, Fox78] This algorithm computes the K shortest paths from s to all the nodes in V (even if we are interested only in the K shortest paths from s to t) Therefore, its best case time complexity is Omega Gamma A K Delta jV j) Shier proposed in [Shie76, Shie79] several methods for the computation of the K shortest paths. In practice, the so called Label Setting algorithm was shown to be the most efficient one. It can be seen as a generalization of Dijkstra s shortest path algorithm and works only in graphs with nonnegative arcs. The time complexity of ....

D. R. Shier: "Iterative Methods for Determining the k Shortest Paths in a Network", Networks, vol. 6, pp. 205--229. (1976)

....minimizing the end to end delay) The routing procedure determines a path that satisfies bandwidth, delay and loss rate requirements of the connection to establish. This procedure limits its search space and thus limits its response time as it uses a constrained modified Double Sweep Algorithm [Shi 76] which finds the k shortest path lengths between a specified node and all other nodes in the graph. It also increases the probability that the connection establishment will be successful as it uses the most recent information on local resource availability. The paper is organized as follows. ....

....and the number of iterations must be bounded since there is no proof of the convergence of the system of equations. 3. Distributed Routing Procedure To solve the mathematical program described above, we propose an extension of one of the kshortest path algorithms (e. g, Double Sweep Algorithm [Shi 76] which finds the k shortest path lengths between a specified node and all other nodes in the graph) The execution order of this algorithm is about , where represents the number of nodes [Eva 78] 3.1 Extension of the Double sweep algorithm The Double sweep algorithm [Min 78, Shi 74, Shi 76] ....

[Article contains additional citation context not shown here]

D.R. Shier, Iterative Methods for Determining the k-Shortest Paths in a Network, Networks, 6, 1976.

....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 ....

D. R. Shier. Iterative methods for determining the k shortest paths in a network. Networks, 6:205--229, 1976.

.... class have to solve a functional equation, that is explicit only when nodes are processed in order of their level in the shortest tree, 12] As an example we point out the classical Dreyfus algorithm, 8] Another class comprises the generalizations of labeling shortest path algorithms of Shier,[16]. Finally, the last class comprises the algorithms based on the path deletion concept due to Martins, 14] A new algorithm, 2] and [3] for the general shortest path ranking problem that uses the path deletion concept is presented. Its theoretical computational complexity is studied and ....

Shier D.A., Iterative methods for determining K shortest paths in a network, Networks 6, (1976), 205--230.

....separately. 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 ....

Shier DR. Iterative methods for determining the k shortest paths in a network. Networks 1976; 6:205--229.

....is discrete. The first algorithms of that kind were considered yet by W. Hoffman and R. Pavley [1] and by R. Bellman and R. Kalaba at the very beginning of dynamic programming [2] The greatest interest was paid to this approach in connection with the problem of the shortest path in a graph [3, 4, 5, 6, 7], and this interest is yet al..ive as it follows from the recent discussion in electronic conferences. The discussion gave some new titles in this field, unfortunately I have no possibility to classify or even to list them now. We consider here a general approach to enumeration of solutions rather ....

....finished. In the other case consider all arcs j 2 N , b(j) i t , and for each j put l j v(i t ) into container e(j) Make container i t passive. This scheme differs from Dijkstra s in one point: his containers include only one value each, currently the best. The container in Shier s algorithm [7] contains a predescribed number K of the best values for each vertex, since it uses the technique of arrays. When the first path is found, all other paths are produced by a standard method: a) activate all containers along the previous path; b) repeate the previous procedure with active containers ....

Shier, D. R. Iterative methods for determining the K shortest paths in a network, Networks, 1976, 6, 205--230.

No context found.

D. R. Shier. Iterative methods for determining the k shortest paths in a network. Networks 6(3):205--229, 1976.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC