U. Zwick. All-pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, 49:289--317, 2002.  Home/Search Document Details and Download
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On the Difficulty of Some Shortest Path Problems - Hershberger, Suri, Bhosle (2003) (1 citation) (Correct)
....model. On the other hand, the o(n ) time all pairs shortest paths algorithms of Fredman [9] does not fit the path comparison model it compares sums of weights of edges that do not necessarily form paths. The matrix multiplication based algorithms by Alon, Galil, Margalit [1] and Zwick [26, 27] also fall outside the path comparison model; however, these algorithm assume the weights lie in a small integer range. Despite its obvious appeal and power, we discovered that the path comparison model also has an unfortunate weakness: adding extra edges to a graph, even ones that obviously do ....
U. Zwick. All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication. In Electronic Colloquium on Computational Complexity, 2000. 13
Finding the k Shortest Simple Paths: A New Algorithm and .. - Hershberger, Maxel, Suri (Correct)
....paths problem in a directed graph has complexity #(m # n) if m = O(n # n) 9] Most known shortest path algorithms, including those by Dijkstra, Bellman Ford and Floyd Warshall, satisfy this model. The exceptions to this model are the matrix multiplication based algorithms by Fredman and others [4, 17, 20]. The same lower bound construction shows that any k simple shortest paths algorithm that finds the best candidate path for each possible branch point o# previously chosen paths is also subject to this lower bound, even for k = 2. All known algorithms for the k simple shortest paths fall into ....
U. Zwick. All pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, 49(3):289--317, 2002.
A New Approach to All-Pairs Shortest Paths on Real-Weighted Graphs - Pettie (2003) (1 citation) (Correct)
....on by Dijkstra [1] Bellman Ford, Floyd Warshall and others (see [2] all work in the comparison addition model with real edge weights. Since then most progress on shortest paths problems has come by assuming integral edge weights. Techniques based on scaling [3 5] integer matrix multiplication [6 10], and fast integer sorting (see [11 15] for recent results) only work with integer edgeweights, and until recently it appeared as though the component hierarchy approach used in [16] and [17] also required integers. We refer the reader to a recent survey paper [18] for more background and ....
U. Zwick, All pairs shortest paths using bridging sets and rectangular matrix multiplication, J. ACM 49 (3) (2002) 289-317.
Dynamic Approximate All-Pairs Shortest Paths In Undirected Graphs - Roditty, Zwick Self-citation (Zwick) (Correct)
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U. Zwick. All-pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, 49:289--317, 2002.
Improved Dynamic Reachability Algorithms for Directed Graphs - Roditty, Zwick (2002) Self-citation (Zwick) (Correct)
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U. Zwick. All-pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, 49:289--317, 2002.
Detecting Short Directed Cycles Using Rectangular Matrix.. - Yuster, Zwick Self-citation (Zwick) (Correct)
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U. Zwick. All-pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, 49:289--317, 2002. 12
On the Difficulty of Some Shortest Path Problems - Hershberger, Suri, Bhosle (2003) (1 citation) (Correct)
No context found.
U. Zwick. All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication. In Electronic Colloquium on Computational Complexity, 2000.
On the Difficulty of Some Shortest Path Problems - Hershberger, Suri, Bhosle (2003) (1 citation) (Correct)
No context found.
U. Zwick. All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication. In Electronic Colloquium on Computational Complexity, 2000. 12
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