D. Eppstein. Finding the k shortest paths. In 35 IEEE FOCS, pages 154-165, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... integer k, and two vertices s and t, the problem asks for the k shortest paths from s to t in increasing order of length, where the paths are required to be simple (loop free) if the paths are allowed to be non simple, then an optimal algorithm is known for both directed and undirected graphs [7]. The best algorithm known for computing the k shortest simple paths in a directed graph is due to Yen [24, 25] The worst case time complexity of his algorithm, using modern data structures, is O(kn(m n log n) in other words, it requires #(n) single source shortest path computations for each ....

....be solved much more e#ciently for DAGs. In particular, our undirected graph algorithms work for DAGs, so the replacement paths problem can be solved in O(m n log n) time for DAGs [11] the k shortest paths problem can be solved in O(k m n log n) time by a method not based on replacement paths [7]. ....

D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28(2):652--673, 1998.

....distance problem, which consists of determining the k distinct shortest distances from s to each vertex q Q. These problems arise in a variety of domains ranging from network routing to speech recognition, where one wishes to find not just the shortest path, but the k shortest paths (see [11, 12] for an extensive bibliography on k shortest paths algorithms) Using the k (distinct) shortest distances from s to q, one can easily find the k (distinct) shortest paths from s to q. The k shortest distance problem is the main problem encountered in most applications such as in speech ....

D. Eppstein, Finding the k Shortest Paths. In: Proc. 35th Symp. Foundations of Computer Science. Inst. of Electrical & Electronics Engineers, November 1994, 154--165.

.... O(m kn log n) time algorithm for this problem has been known since 1975 [3] a recent improvement by Eppstein essentially achieves the optimal time of O(m n log n k) the algorithm computes an implicit representation of the paths, from which each path can be output in O(n) additional time [2]. t s a b c d e g h 10 1 1 1 1 10 11 1 1 1 1 Figure 1: The di#erence between simple and nonsimple k shortest paths. The three simple shortest paths have lengths 6, 20 and 21, respectively. Without the simplicity constraint, paths may use the cycles (a, b, a) and (d, e, d) giving ....

D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28(2):652--673, 1998.

....LS information is inaccurate. In contrast to that approach, we propose to dissipate the possible inaccuracy of the state information concerning a single link by admitting multiple paths between a given source destination pair. Several papers discuss the algorithms for finding shortest paths [10], 22] Our solutions are based on the algorithm presented in [22] which we have modified to find best one to all loopless paths. THE ROUTING MODEL Link state routing requires each router to maintain a link state database, which is essentially a map of the network topology with associated ....

D. Eppstein. Finding the K Shortest Paths. SIAM J. Computing, 28:652--673, 1999.

....nodes by many edges, and in that sense our problem appears to be more difficult. All the known methods for shortest path sensitivity analysis seem to require Omega Gamma m) work per shortest path edge [1] Our problem also has some similarity to the k shortest paths problem studied by Eppstein [4], but requires different techniques. 3 Mechanism Design and Network Routing In order to provide the economic context for our problem, we briefly discuss the topic of mechanism design and the Vickrey Clarke Groves payment scheme. We cover only the most relevant concepts, and try to motivate them ....

D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28:652--673, 1998.

....about 20 basic reactions representing dehydrogenase, kinase, and other common enzymes. All edges are assigned weights, whose biological interpretation is a likelihood of the corresponding reaction. The computation of pathways in this graph is realized with k shortest paths algorithm by Eppstein [1]. 3 Result and Discussion Currently, over 700 compounds are stored in the database, and the search process can e#ciently compute pathways. For example, it can reproduce glycolysis and amino acid syntheses in bacteria. The advantage of our system is the enumeration of all the logically possible ....

Eppstein, D., Finding the k Shortest Paths, Proceedings FOCS '94, 154--165, 1994.

....about 20 basic reactions representing dehydrogenase, kinase, and other common enzymes. All edges are assigned weights, whose biological interpretation is a likelihood of the corresponding reaction. The computation of pathways in this graph is realized with k shortest paths algorithm by Eppstein [1]. 3 Result and Discussion Currently, over 700 compounds are stored in the database, and the search process can efficiently compute pathways. For example, it can reproduce glycolysis and amino acid syntheses in bacteria. The advantage of our system is the enumeration of all the logically possible ....

Eppstein, D., Finding the k Shortest Paths, Proceedings FOCS '94, 154--165, 1994.

....on this paper was partially supported by National Science Foundation grants CCR 9901958 and ANI 9813723. a unifying framework for many optimization problems such as knapsack, sequence alignment in molecular biology, inscribed polygon construction, and length limited Huffmancoding, etc. Eppstein [4] is a good reference for shortest paths and their applications. Most complex applications of the shortest path problem, however, require more than just the calculation of a single shortest path. In some applications, the desired path might be subject to additional constraints that are hard to ....

....deleting an edge, and then finding the new shortest path. To the best of our knowledge, all the known methods for this type of sensitivity analysis of shortest paths require m) work per shortest path edge [1] Our problem also has some similarity to the k shortest paths problem studied by Eppstein [4], but requires different techniques. Finally, Bikhchandani et al. 2] and Schummer and Vohra [18] have considered general auction settings where the Vickrey payments correspond to dual variables in a linear program. Their results depend on a combinatorial condition, which they call the agents ....

D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28:652--673, 1998.

....methods. We have applied the KMCSP algorithm in SPIDER, a web based optical network design tool [9] In the case of single metric, the KMCSP problem becomes a problem of finding K Shortest Paths (KSP) from one source node to one target node. The KSP problem has many practical applications [10][11]. In multiple constrained metrics case, both the MCSP and the KMCSP problems are known to be NPcomplete [3] 4] 12] 14] Most of the current approaches are concentrated on developing efficient polynomial or pseudo polynomial time algorithms to give feasible or approximate solutions to MCSP ....

D. Eppstein. Finding the k shortest Paths. SIAM J. Computing, 28(2):652673. 1999.

....also present Validation and Veri cation results for each step. 3.3.1 Finding Multiple Paths As a rst step we need to nd and store for each source multiple paths to every destination. Various algorithms can be used to compute multiple paths from a source to a destination. We used a method from [Epp94] which nds multiple short paths connecting two vertices in a graph (allowing repeated vertices and edges in the paths) in constant time per path after a preprocessing stage dominated by a single source shortest path computation. We extended a sample implementation from [Gra] to read the topology ....

D. Eppstein. Finding the k shortest paths. In 35th IEEE Symp. Foundations of Computer Science, pages 154-165, February 1994.

....researchers have resorted to several heuristics and approximation algorithms. 2 One common approach to the RSP problem is to find the k shortest paths w.r.t. a cost function defined based on the link weights and the given constraint, hoping that one of these paths is feasible and near optimal [20, 32, 15, 19]. The value of k determines the performance and overhead of this approach; if k is large, the algorithm has good performance but its computational cost is prohibitive. A similar approach to the k shortest paths is to implicitly enumerate all feasible paths [3] but this approach is also ....

D. Eppstein. Finding the k shortest paths. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 154 -- 165. IEEE, Nov. 1994.

....of shortest paths from any given source vertex to all other vertices of the graph G = V; E) with n vertices and m edges. Early implementation of Dijkstra s algorithm required time O(n 2 ) or O(m lg n) Fredman and Tarjan [4] gave O(m n lg n) implementation using Fibonacci heaps. Eppstein [3] consider the problem of computing k shortest paths from a source in a weighted digraph. His algorithm takes O(m n log n k) time. Our shortest path problem is different from the one of Eppstein in that we look for the vertex disjoint paths with lexicographically smallest sequence of weights. ....

Eppstein, D.: Finding the k shortest paths. SIAM J. Computing, 28 (2) (1999) 652--673

....Observe that although there are 2 k neighbor configurations, it is easy to find the highest probability configuration in time O(k log k kj Gammaj) time via a shortest path computation. It also turns out that we can extract the shortest P paths in time O(kj Gammaj k log k P log P ) [11]. We have not observed any adverse effects of such truncation of (10) on the accuracy of classification. Typically, after the top two or three class choices, the remaining classes have probabilities as low as 10 Gamma30 and can be ignored. On the other hand, the large range of numbers ....

D. Eppstein. Finding the k shortest paths. In Symposium on the Foundations of Computer Science. IEEE, 1994.

....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 developed for them. Yen [45] gives an algorithm for the significantly harder problem of finding the k shortest ....

....a measure ffi(u; v) of the extra distance added to the length of a path from u to t if the edge (u; v) is used instead of taking the optimal path from u to t: ffi(u; v) w(u; v) dist(v; t) Gamma dist(u; t) The following lemma describes some properties of this measure. Lemma 3. 1 (Eppstein [13]) i) ffi(u; v) 0 for all (u; v) 2 E (ii) ffi(u; v) 0 for all (u; v) 2 T (iii) For any path p from s to t, weight(p) dist(s; t) X (u;v)2p ffi(u; v) dist(s; t) X (u;v)2sidetracks(p) ffi(u; v) Proof: i) Since dist(u; t) is the weight of the shortest path from u to t, dist(u; t) ....

[Article contains additional citation context not shown here]

David Eppstein. Finding the k shortest paths. In Proc. 35th IEEE Symposium on Foundations of Computer Science, pages 154--165, 1994.

....calculation algorithms that calculate suffix matching path sets. Several existing multipath algorithms generate suffix matched paths. Here we show that the k ranked path algorithm [6] produces suffix matched paths. Proposition: The unconstrained k shortest (ranked) simple paths algorithm [6, 7] produces suffix matched path sets. Proof: The unconstrained k shortest path algorithm uses the following invariant for computing multiple paths between all pairs of nodes in the network. A path of rank k between node x 1 and xn is composed of subpaths all of whose ranks are k. Since each node ....

D. Eppstein. Finding the k shortest paths. In Proc. 35th Symp. Foundations of Computer Science, pages 154--165. Inst. of Electrical & Electronics Engineers, November 1994.

....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 Eppstein s algorithm, in O(m n log n nk) ....

....v) dist(v; t) Gamma dist(u; t) The following lemma describes some properties of this measure. 2 1 t a b c d e f s g 2 3 4 1 1 2 1 3 4 2 4 (a) Solid edges form the tree T t a b c d e f s g 4 2 3 0 5 (b) Values of ffi are shown for non tree edges Fig. 1. an example graph Lemma 1 (Eppstein [7]) i) ffi (u; v) 0 for all (u; v) 2 E. ii) ffi (u; v) 0 for all (u; v) 2 T . iii) For any path p from s to t, weight(p) dist(s; t) X (u;v)2p ffi (u; v) dist(s; t) X (u;v)2sidetracks(p) ffi (u; v) To find the k shortest paths from s to t, it is therefore sufficient to find ....

[Article contains additional citation context not shown here]

David Eppstein. Finding the k shortest paths. In Proc. 35th IEEE Symposium on Foundations of Computer Science, pages 154--165, 1994.

No context found.

D. Eppstein. Finding the k shortest paths. In 35 IEEE FOCS, pages 154-165, 1994.

No context found.

D. Eppstein. Finding the k shortest paths. In Proc. of the 35th Annual Symposium on Foundations of Computer Science, pages 154--155, November 1994.

No context found.

D. Eppstein. Finding the k shortest paths. In In Proc. of the 35th Annual Symposium on Foundations of Computer Science, pages 154--155, November 1994.

No context found.

David Eppstein. Finding the k shortest paths. In Proc. 35th Symp. Foundations of Computer Science, pages 154--165. IEEE, November 1994.

No context found.

D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28(2):652--673, 1998.

No context found.

D. Eppstein. Finding the k shortest paths. SIAM J. Computing, 28(2):652-673, 1998.

No context found.

David Eppstein. Finding the k shortest paths. SIAM J. Computing, 28(2):652--673, 1998.

No context found.

David Eppstein. 1994. Finding the k shortest paths.

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