Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Integer and combinatorial optimization
Integer and combinatorial optimization
Planar graph decomposition and all pairs shortest paths
Journal of the ACM (JACM)
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Communications of the ACM
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Flows in Networks
Spatially modelling pathways of migratory birds for nature reserve site selection
International Journal of Geographical Information Science
The Plexus Model for the Inference of Ancestral Multidomain Proteins
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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In a large, dense network, the computation of the 'distances', i.e., the shortest path lengths between all pairs of nodes, can take a long time with algorithms known from the literature. We present two all-pairs shortest path algorithms, based on the equations of Bellman. These algorithms run fast, much faster than indicated by their time complexity bound of O(n^2m), where n is the number of nodes and m the number of arcs. As in Bellman's method 'candidate' distances are maintained and updated, obtaining the distances eventually. However, the order of updating the candidate distances is changed, in such a way that arcs are eliminated as soon as it is clear that they are not relevant for the update of candidate distances later in the algorithm. In dense graphs this can significantly reduce the computation time. By scanning the arcs in order of increasing weight, arcs are eliminated earlier. By scanning the nodes in a 'pseudo-topological' order, the computation time can further decrease. In acyclic directed networks one of the resulting all-pairs algorithms runs in O(mlogn+nm"0) time, where m"0 denotes the number of 'essential' arcs, i.e., arcs that are indispensable in some shortest path.