Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
Artificial Intelligence - Special issue on knowledge representation
Shortest path algorithms: a computational study with the C programming language
Computers and Operations Research
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
All-pairs-shortest-length on strongly chordal graphs
Discrete Applied Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Unified all-pairs shortest path algorithms in the chordal hierarchy
Discrete Applied Mathematics
Journal of the ACM (JACM)
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Backtracking algorithms for disjunctions of temporal constraints
Artificial Intelligence
Communications of the ACM
Introduction to algorithms
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Fully dynamic all pairs shortest paths with real edge weights
Journal of Computer and System Sciences - Special issue on FOCS 2001
A note of an O(n3/logn) time algorithm for all pairs shortest paths
Information Processing Letters
Journal of Artificial Intelligence Research
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
ACM Transactions on Algorithms (TALG)
Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Contraction hierarchies: faster and simpler hierarchical routing in road networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
The Knowledge Engineering Review
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
Solving temporal problems using SMT: strong controllability
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n2wd) time, where wd is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(nw2d + n2sd) on general graphs, where sd ≤ wd is the size of the largest minimal separator induced by the vertex ordering d. We show empirically that on both constructed and realistic benchmarks, in many cases the algorithms outperform Floyd-Warshall's as well as Johnson's algorithm, which represent the current state of the art with a run time of O(n3) and O(nm + n2 log n), respectively. Our algorithms can be used for spatial and temporal reasoning, such as for the Simple Temporal Problem, which underlines their relevance to the planning and scheduling community.