How to multiply matrices faster
How to multiply matrices faster
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
High probability parallel transitive-closure algorithms
SIAM Journal on Computing
A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
Witnesses for Boolean matrix multiplication and for transitive closure
Journal of Complexity
Finding the hidden path: time bounds for all-pairs shortest paths
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)
All pairs shortest paths for graphs with small integer length edges
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
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
Rectangular matrix multiplication revisited
Journal of Complexity
Fast rectangular matrix multiplication and applications
Journal of Complexity
All pairs lightest shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
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)
Floats, integers, and single source shortest paths
Journal of Algorithms
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
Fully dynamic biconnectivity and transitive closure
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algebraic Complexity Theory
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Journal of the ACM (JACM)
Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O(n2 barrier
Journal of the ACM (JACM)
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
Answering distance queries in directed graphs using fast matrix multiplication
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
A new algorithm for optimal 2-constraint satisfaction and its implications
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Fully dynamic all pairs shortest paths with real edge weights
Journal of Computer and System Sciences - Special issue on FOCS 2001
On the difficulty of some shortest path problems
ACM Transactions on Algorithms (TALG)
Algorithmic Techniques for Maintaining Shortest Routes in Dynamic Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
Faster algorithms for finding lowest common ancestors in directed acyclic graphs
Theoretical Computer Science
All-pairs bottleneck paths for general graphs in truly sub-cubic time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
All-pairs bottleneck paths in vertex weighted graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the k shortest simple paths: A new algorithm and its implementation
ACM Transactions on Algorithms (TALG)
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
All-pairs disjoint paths from a common ancestor in Õ(nω) time
Theoretical Computer Science
Language constrained graph problems: a microcosm of engineering research and development
CEA'08 Proceedings of the 2nd WSEAS International Conference on Computer Engineering and Applications
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
Discounted deterministic Markov decision processes and discounted all-pairs shortest paths
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
On-line exact shortest distance query processing
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Computational study on planar dominating set problem
Theoretical Computer Science
Discounted deterministic Markov decision processes and discounted all-pairs shortest paths
ACM Transactions on Algorithms (TALG)
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)
Nondecreasing paths in a weighted graph or: How to optimally read a train schedule
ACM Transactions on Algorithms (TALG)
Algorithms and theory of computation handbook
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
SIAM Journal on Computing
Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs
SIAM Journal on Computing
All-pairs shortest paths with a sublinear additive error
ACM Transactions on Algorithms (TALG)
A shortest cycle for each vertex of a graph
Information Processing Letters
An experimental study on approximating K shortest simple paths
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximate shortest paths in weighted graphs
Journal of Computer and System Sciences
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Efficient algorithms for the 2-center problems
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Automatica (Journal of IFAC)
Replacement paths and k simple shortest paths in unweighted directed graphs
ACM Transactions on Algorithms (TALG)
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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
All-pairs ancestor problems inweighted dags
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Graph expansion analysis for communication costs of fast rectangular matrix multiplication
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
Semi-metric Networks for Recommender Systems
WI-IAT '12 Proceedings of the The 2012 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Volume 03
Fast approximation algorithms for the diameter and radius of sparse graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Finding the minimum-weight k-path
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Social network analysis for customer churn prediction
Applied Soft Computing
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We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms.The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in Õ(n2+μ) time, where μ satisfies the equation ω(1, μ, 1) = 1 + 2μ and ω(1, μ, 1) is the exponent of the multiplication of an n × nμ matrix by an nμ × n matrix. Currently, the best available bounds on ω(1, μ, 1), obtained by Coppersmith, imply that μ O(n2.575). Our algorithm improves on the &Otilede;(n(3c+ω)/2) time algorithm, where ω = ω(1, 1, 1) O(n2.688).The second algorithm solves the APSP problem almost exactly for directed graphs with arbitrary nonnegative real weights. The algorithm runs in Õ((nω/&epsis;) log(W/&epsis;)) time, where &epsis; 0 is an error parameter and W is the largest edge weight in the graph, after the edge weights are scaled so that the smallest non-zero edge weight in the graph is 1. It returns estimates of all the distances in the graph with a stretch of at most 1 + &epsis;. Corresponding paths can also be found efficiently.