Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Faster scaling algorithms for network problems
SIAM Journal on Computing
Faster algorithms for the shortest path problem
Journal of the ACM (JACM)
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
Scaling Algorithms for the Shortest Paths Problem
SIAM Journal on Computing
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
On the exponent of the all pairs shortest path problem
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
All pairs shortest distances for graphs with small integer length edges
Information and Computation
Finding real-valued single-source shortest paths in o(n3 expected time
Journal of Algorithms
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)
Information Bounds Are Weak in the Shortest Distance Problem
Journal of the ACM (JACM)
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
Improved fast integer sorting in linear space
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Introduction to Algorithms
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Equivalence between Priority Queues and Sorting
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
An Inverse-Ackermann Style Lower Bound for the Online Minimum Spanning Tree
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the Comparison-Addition Complexity of All-Pairs Shortest Paths
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Experimental Evaluation of a New Shortest Path Algorithm
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Effect of Algebraic Structure on the Computational Complexity of Matrix Multiplication
The Effect of Algebraic Structure on the Computational Complexity of Matrix Multiplication
Efficient algorithms for solving shortest paths on nearly acyclic directed graphs
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
Solving shortest paths efficiently on nearly acyclic directed graphs
Theoretical Computer Science
Two fast algorithms for all-pairs shortest paths
Computers and Operations Research
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the K-simple shortest paths problem in weighted directed graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Terracost: Computing least-cost-path surfaces for massive grid terrains
Journal of Experimental Algorithmics (JEA)
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
Improved algorithms for the k simple shortest paths and the replacement paths problems
Information Processing Letters
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Design and Engineering of External Memory Traversal Algorithms for General Graphs
Algorithmics of Large and Complex Networks
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
The Floyd--Warshall algorithm on graphs with negative cycles
Information Processing Letters
Faster algorithms for all-pairs small stretch distances in weighted graphs
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Nondecreasing paths in a weighted graph or: How to optimally read a train schedule
ACM Transactions on Algorithms (TALG)
A simpler algorithm for the all pairs shortest path problem with o(n2 log n) expected time
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
SIAM Journal on Computing
On the $k$ Shortest Simple Paths Problem in Weighted Directed Graphs
SIAM Journal on Computing
Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs
SIAM Journal on Computing
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Networks cannot compute their diameter in sublinear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
All-pairs nearly 2-approximate shortest-paths in O(n2 polylog n) time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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
On the round-trip 1-center and 1-median problems
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
Computing all-pairs shortest paths by leveraging low treewidth
Journal of Artificial Intelligence Research
A simplified algorithm for the all pairs shortest path problem with O(n2logn) expected time
Journal of Combinatorial Optimization
Sharing information in all pairs shortest path algorithms
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Sharing information in all pairs shortest path algorithms
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
All-pairs shortest paths in O(n2) time with high probability
Journal of the ACM (JACM)
Efficient algorithms for the all pairs shortest path problem with limited edge costs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Fast shortest-paths algorithms in the presence of few destinations of negative-weight arcs
Journal of Discrete Algorithms
Sharing information for the all pairs shortest path problem
Theoretical Computer Science
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We present a new all-pairs shortest path algorithm that works with real-weighted graphs in the traditional comparison-addition model. It runs in O(mn + n2 log log n) time, improving on the long-standing bound of O(mn + n2 log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Here m and n are the number of edges and vertices, respectively.Our algorithm is rooted in the so-called component hierarchy approach to shortest paths invented by Thorup for integer-weighted undirected graphs, and generalized by Hagerup to integer-weighted directed graphs. The technical contributions of this paper include a method for approximating shortest path distances and a method for leveraging approximate distances in the computation of exact ones. We also provide a simple, one line characterization of the class of hierarchy-type shortest path algorithms. This characterization leads to some pessimistic lower bounds on computing single-source shortest paths with a hierarchy-type algorithm.