The input/output complexity of sorting and related problems
Communications of the ACM
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
I/O-complexity of graph algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Cache-oblivious priority queue and graph algorithm applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Buffer Tree: A New Technique for Optimal I/O-Algorithms (Extended Abstract)
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
External-Memory Breadth-First Search with Sublinear I/O
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Improved Algorithms and Data Structures for Solving Graph Problems in External Memory
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
Cache-oblivious shortest paths in graphs using buffer heap
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
On Trade-Offs in External-Memory Diameter-Approximation
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Design and Engineering of External Memory Traversal Algorithms for General Graphs
Algorithmics of Large and Complex Networks
Reducing the memory required to find a geodesic shortest path on a large mesh
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
I/O-efficient shortest path algorithms for undirected graphs with random or bounded edge lengths
ACM Transactions on Algorithms (TALG)
I/O-efficient hierarchical diameter approximation
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We present several new external-memory algorithms for finding all-pairs shortest paths in a V-node. E-edge undirected graph. For all-pairs shortest paths and diameter in unweighted undirected graphs we present cache-oblivious algorithms with O(V·E/B log M/B E/B) I/Os, where B is the block-size and M is the size of internal memory. For weighted undirected graphs we present a cache-aware APSP algorithm that performs O(V·(√VE/B+E/B log E/B)) I/Os. We also present efficient cache-aware algorithms that find paths between all pairs of vertices in an unweighted graph with lengths within a small additive constant of the shortest path length.All of our results improve earlier results known for these problems. For approximate APSP we provide the first nontrivial results. Our diameter result uses O(V + E) extra space, and all of our other algorithms use O(V2) space.