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B. L. Fox: "Calculating kth Shortest Paths", INFOR, vol. 11, no. 1, pp. 66--70. (1973)

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An Algorithm for Efficient Computation of K Shortest Paths - Jimenez, Marzal (1994)   (1 citation)  (Correct)

....similar to the Bellman Ford algorithm. Dreyfus [Drey69] extended the Bellman Kalaba equations to the general case and proposed important improvements to the method of resolution. The time complexity of the Dreyfus algorithm is O(A K Delta jV j Delta 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 ....

B. L. Fox: "Calculating kth Shortest Paths", INFOR, vol. 11, no. 1, pp. 66--70. (1973)


Finding the k Shortest Paths in Parallel - Ruppert (2000)   (Correct)

....work to compute the k shortest paths, once the shortest paths are known. The problem of finding the k shortest paths in sequential models of computation was discussed as early as 1959 by Hoffman and Pavley [14] Fox presents an algorithm that can be implemented to run in O(m kn log n) time [9]. Eppstein s recent sequential algorithm [7] is a significant improvement. It computes an implicit representation of the k shortest paths for a given source and destination in O(m n log n k) time. The k shortest paths to a given destination from every vertex in the graph can be found, ....

B. L. Fox. Calculating kth shortest paths. INFOR; Canadian Journal of Operational Research, 11(1):66-- 70, 1973.


Alignment of Phonetic Sequences - Kondrak (1999)   (1 citation)  (Correct)

....it even for relatively small data sets. In response to the second argument it can be pointed out that a simple modification the basic DP algorithm will produce all alignments that are within ffl of the optimal distance (Myers, 1995) By applying methods from the operations research 13 literature (Fox, 1973), the algorithm can be adapted to deliver the n best solutions. Both of these modifications preserve the algorithm s polynomial complexity. The third argument is somewhat hypothetical because Covington s algorithm handles neither metathesis nor assimilation. It remains to be seen if incorporating ....

Fox, B. L. (1973). Calculating the Kth shortest paths. INFOR -- Canadian Journal of Operational Research and Information Processing, 11(1):66--70.


Parallel Algorithms for the k Shortest Paths and Related Problems - Ruppert   (Correct)

....o(n 3 ) work. The problem of finding the k shortest paths between vertices in a graph has long been studied in sequential models of computation. The problem was discussed as early as 1959 by Hoffman and Pavley [23] Fox presents an algorithm that can be implemented to run in O(m kn log n) time [17]. Eppstein s recent sequential algorithm computes the k shortest paths for a given source and destination [13] in O(m n log n k) time. This algorithm will be described in Section 3.2, below. Other variations of the k shortest path problem have been studied and sequential algorithms have been ....

B. L. Fox. Calculating kth shortest paths. INFOR; Canadian Journal of Operational Research, 11(1):66--70, 1973.


Finding the k Shortest Paths in Parallel - Ruppert   (Correct)

....and work to compute the k shortest paths, once the shortest paths are known. The problem of finding the k shortest paths in sequential models of computation was discussed as early as 1959 by Hoffman and Pavley [14] Fox presents an algorithm that can be implemented to run in O(m kn log n) time [9]. Eppstein s recent sequential algorithm [7] is a significant improvement. It computes an implicit representation of the k shortest paths for a given source and destination in O(m n log n k) time. The k shortest paths to a given destination from every vertex in the graph can be found, using ....

B. L. Fox. Calculating kth shortest paths. INFOR; Canadian Journal of Operational Research, 11(1):66--70, 1973.


A New Algorithm for the Alignment of Phonetic Sequences - Kondrak (2000)   (3 citations)  (Correct)

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Bennett L. Fox. 1973. Calculating the Kth shortest paths. INFOR -- Canadian Journal of Operational Research and Information Processing, 11(1):66--70.

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