Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
The input/output complexity of sorting and related problems
Communications of the ACM
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Shortest path queries in planar graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On external memory graph traversal
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
I/O-optimal algorithms for planar graphs using separators
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Shortest Paths and Distances in Planar Graphs
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Shortest Path Queries in Digraphs of Small Treewidth
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
On-Line Algorithms for Shortest Path Problems on Planar Digraphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
I/O-efficient topological sorting of planar DAGs
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
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)
I/O-Efficient Strong Connectivity and Depth-First Search for Directed Planar Graphs
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On external-memory MST, SSSP and multi-way planar graph separation
Journal of Algorithms
An external memory data structure for shortest path queries (extended abstract)
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
I/O-efficient algorithms for computing planar geometric spanners
Computational Geometry: Theory and Applications
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
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
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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In this paper we present space-query trade-offs for external memory data structures that answer shortest path queries on planar directed graphs. For any $S = {\it \Omega}(N^{1 + \epsilon}$) and S=O(N2/B), our main result is a family of structures that use S space and answer queries in $O({{N^{2}}\over{SB}})$I/Os, thus obtaining optimal space-query product O(N2/B). An S space structure can be constructed in $O(\sqrt{S}\cdot {\rm sort}(N))$ I/Os, where sort(N) is the number of I/Os needed to sort N elements, B is the disk block size, and N is the size of the graph.