Fast approximation of centrality
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximate distance oracles for geometric graphs
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)
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
On the Power of BFS to Determine a Graphs Diameter
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Computing Shortest Paths with Uncertainty
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Estimating All Pairs Shortest Paths in Restricted Graph Families: A Unified Approach
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Efficient algorithms for constructing (1+,ε, β)-spanners in the distributed and streaming models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Journal of the ACM (JACM)
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
External-memory exact and approximate all-pairs shortest-paths in undirected graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Spanners and emulators with sublinear distance errors
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)
O(1) query time algorithm for all pairs shortest distances on permutation graphs
Discrete Applied Mathematics
Computing shortest paths with uncertainty
Journal of Algorithms
Approximate distance oracles for graphs with dense clusters
Computational Geometry: Theory and Applications
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & 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
Spanners for bounded tree-length graphs
Theoretical Computer Science
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
All-pairs nearly 2-approximate shortest paths in O(n2polylogn) time
Theoretical Computer Science
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
ACM Transactions on Algorithms (TALG)
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Discovery of network properties with all-shortest-paths queries
Theoretical Computer Science
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
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
All-pairs shortest paths with a sublinear additive error
ACM Transactions on Algorithms (TALG)
An experimental study on approximating K shortest simple paths
ESA'11 Proceedings of the 19th European conference on Algorithms
On approximate distance labels and routing schemes with affine stretch
DISC'11 Proceedings of the 25th international conference on Distributed computing
Fast and simple approximation of the diameter and radius of a graph
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Subquadratic time approximation algorithms for the girth
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
Deterministic constructions of approximate distance oracles and spanners
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
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate distance oracles for graphs with dense clusters
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Efficient processing of distance queries in large graphs: a vertex cover approach
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Optimal distributed all pairs shortest paths and applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
Improved approximation algorithms for maximum lifetime problems in wireless networks
Theoretical Computer Science
Distributed algorithms for network diameter and girth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Faster approximation of distances in graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Fault tolerant additive spanners
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
ACM Transactions on Algorithms (TALG)
Efficient distributed source detection with limited bandwidth
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Efficient single-source shortest path and distance queries on large graphs
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast approximation algorithms for the diameter and radius of sparse graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Approximating the diameter of planar graphs in near linear time
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Fast approximation of betweenness centrality through sampling
Proceedings of the 7th ACM international conference on Web search and data mining
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In the recent past, there has been considerable progress in devising algorithms for the all-pairs shortest paths (APSP) problem running in time significantly smaller than the obvious time bound of O(n3). Unfortunately, all the new algorithms are based on fast matrix multiplication algorithms that are notoriously impractical. Our work is motivated by the goal of devising purely combinatorial algorithms that match these improved running times. Our results come close to achieving this goal, in that we present algorithms with a small additive error in the length of the paths obtained. Our algorithms are easy to implement, have the desired property of being combinatorial in nature, and the hidden constants in the running time bound are fairly small.Our main result is an algorithm which solves the APSP problem in unweighted, undirected graphs with an additive error of 2 in time $O(n^{2.5}\sqrt{\log n})$. This algorithm returns actual paths and not just the distances. In addition, we give more efficient algorithms with running time {\footnotesize $O(n^{1.5} \sqrt{k \log n} + n^2 \log^2 n)$} for the case where we are only required to determine shortest paths between k specified pairs of vertices rather than all pairs of vertices. The starting point for all our results is an $O(m \sqrt{n \log n})$ algorithm for distinguishing between graphs of diameter 2 and 4, and this is later extended to obtaining a ratio 2/3 approximation to the diameter in time $O(m \sqrt{n \log n} + n^2 \log n)$. Unlike in the case of APSP, our results for approximate diameter computation can be extended to the case of directed graphs with arbitrary positive real weights on the edges.