Computational geometry: an introduction
Computational geometry: an introduction
Shortest paths in Euclidean graphs
Algorithmica
Clique partitions, graph compression and speeding-up algorithms
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On the exponent of the all pairs shortest path problem
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the all-pairs-shortest-path problem
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Journal of the ACM (JACM)
Improved parallel integer sorting without concurrent writing
Information and Computation
All pairs lightest shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Fly cheaply: on the minimum fuel consumption problem
Journal of Algorithms
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Almost tight upper bounds for vertical decompositions in four dimensions
Journal of the ACM (JACM)
Improved algorithm for all pairs shortest paths
Information Processing Letters
A Shortest Path Algorithm for Real-Weighted Undirected Graphs
SIAM Journal on Computing
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
Finding a maximum weight triangle in n3-Δ time, with applications
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Colored intersection searching via sparse rectangular matrix multiplication
Proceedings of the twenty-second annual symposium on Computational geometry
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
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding a heaviest triangle is not harder than matrix multiplication
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the smallest H-Subgraph in real weighted graphs and related problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
All-pairs bottleneck paths for general graphs in truly sub-cubic time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Subcubic algorithms for recursive state machines
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Nondecreasing paths in a weighted graph or: how to optimally read a train schedule
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
Faster algorithms for guided tree edit distance
Information Processing Letters
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Efficient algorithms on sets of permutations, dominance, and real-weighted APSP
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Efficient approximation algorithms for shortest cycles in undirected graphs
Information Processing Letters
Sparse RNA Folding: Time and Space Efficient Algorithms
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Faster Regular Expression Matching
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Computing the dilation of edge-augmented graphs in metric spaces
Computational Geometry: Theory and Applications
A (slightly) faster algorithm for Klee's measure problem
Computational Geometry: Theory and Applications
The Floyd--Warshall algorithm on graphs with negative cycles
Information Processing Letters
A sub-cubic time algorithm for the k-maximum subarray problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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
Efficient approximation algorithms for shortest cycles in undirected graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Finding heaviest H-subgraphs in real weighted graphs, with applications
ACM Transactions on Algorithms (TALG)
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Nondecreasing paths in a weighted graph or: How to optimally read a train schedule
ACM Transactions on Algorithms (TALG)
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast distance multiplication of unit-Monge matrices
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Reducing the worst case running times of a family of RNA and CFG problems, using Valiant's approach
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
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
Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs
SIAM Journal on Computing
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
All-pairs shortest paths with a sublinear additive error
ACM Transactions on Algorithms (TALG)
Edit distance with duplications and contractions revisited
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Faster Algorithms for Max-Product Message-Passing
The Journal of Machine Learning Research
A shortest cycle for each vertex of a graph
Information Processing Letters
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Running time analysis of Ant Colony Optimization for shortest path problems
Journal of Discrete Algorithms
Approximate shortest paths in weighted graphs
Journal of Computer and System Sciences
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Efficient algorithms for the 2-center problems
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
On the round-trip 1-center and 1-median problems
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
Faster approximation of distances in graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
A simplified algorithm for the all pairs shortest path problem with O(n2logn) expected time
Journal of Combinatorial Optimization
Fast shortest-paths algorithms in the presence of few destinations of negative-weight arcs
Journal of Discrete Algorithms
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In the first part of the paper, we reexamine the all-pairsshortest paths (APSP) problem and present a newalgorithm with running time approaching O(n3/log2n), which improves all known algorithms for general real-weighted dense graphs andis perhaps close to the best result possible without using fast matrix multiplication, modulo a few log log n factors. In the second part of the paper, we use fast matrix multiplication to obtain truly subcubic APSP algorithms for a large class of "geometrically weighted" graphs, where the weight of an edge is a function of the coordinates of its vertices. For example, for graphs embedded in Euclidean space of a constant dimension d, we obtain a time bound near O(n3-(3-Ω)/(2d+4)), where Ω 2.922). Our framework greatly extends the previously considered case of small-integer-weighted graphs, and incidentally also yields the first truly subcubic result (near O(n3-(3-Ω)/4)=O(n2.844) time) forAPSP in real-vertex-weighted graphs, as well as an improved result (near O(n(3+Ω)/2)=O(n2.688) time) for the all-pairs lightest shortest path problem for small-integer-weighted graphs.