Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Mixed-approach algorithms for transitive closure (extended abstract)
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
A Note on Dijkstra's Shortest Path Algorithm
Journal of the ACM (JACM)
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Communications of the ACM
Introduction to Algorithms
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Improved algorithm for all pairs shortest paths
Information Processing Letters
A Shortest Path Algorithm for Real-Weighted Undirected Graphs
SIAM Journal on Computing
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An O(n3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An O(n3loglogn/logn) time algorithm for the all-pairs shortest path problem
Information Processing Letters
ACM Transactions on Algorithms (TALG)
All-pairs shortest paths with real weights in O(n3/ log n) time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
An O(n3 log log n/ log2 n) time algorithm for all pairs shortest paths
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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In this paper we present hybrid algorithms for the single-source shortest-paths (SSSP) and for the all-pairs shortest-paths (APSP) problems, which are asymptotically fast when run on graphs with few destinations of negative-weight arcs. Plainly, the case of graphs with few sources of negative-weight arcs can be handled as well, using reverse graphs. With a directed graph with n nodes and m arcs, our algorithm for the SSSP problem has an O(@?(m+nlogn+@?^2))-time complexity, where @? is the number of destinations of negative-weight arcs in the graph. In the case of the APSP problem, we propose an O(nm^@?+n^2logn+@?n^2) algorithm, where m^@? is the number of arcs participating in shortest paths. Notice that m^@? is likely to be small in practice, since m^@?=O(nlogn) with high probability for several probability distributions on arc weights.