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## External Data Structures for Shortest Path Queries on Planar Digraphs

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### Citations

590 |
The input/output complexity of sorting and related problems
- Aggarwal, Vitter
- 1988
(Show Context)
Citation Context ...tensively studied in internal memory [7, 13, 12, 10, 9], this is the first result of its type in external memory. 1.1 I/O-Model and Related Work We will be working in the standard two-level I/O model =-=[1]-=-, where M is the number of vertices that can fit into internal memory, and B is the number of vertices that can fit into a disk block, with1 M<Nand 1 ≤ B ≤ M/2. An I/O is the operation of transferring... |

456 | A separator theorem for planar graphs
- Lipton, Tarjan
- 1977
(Show Context)
Citation Context ...N)-separator of an N-vertex graph G =(V,E) is a subset VS of the vertices V of size f(N), such that the removal of VS partitions G into two subgraphs G1 and G2 of size at most 2N/3. Lipton and Tarjan =-=[18]-=- showed that any planarsExternal Data Structures for Shortest Path Queries on Planar Digraphs 331 01 00 11 01 01 00 11 01 0 0 1 1 00 11 0 00 11 0 1 1 01 00 11 00 11 00 11 00 11 01 01 00 11 01 00 11 00... |

182 | Externalmemory graph algorithms
- Chiang, Goodrich, et al.
- 1995
(Show Context)
Citation Context ... for SSSP, as well the best algorithms for the simpler BFS and DFS problems, use Ω(|V |) I/Os.Moreprecisely, their I/O-complexity is O(min{(|V | + |E|/B) · log |V | +sort(|E|), |V | + |V | |E| M B }) =-=[8,11,17]-=- . However, improved algorithms have been developed for planar digraphs [5, 6,3]. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these alg... |

163 |
Data structures for on-line updating of minimum spanning trees, with applications
- Frederickson
- 1985
(Show Context)
Citation Context ...ct is O(N 2 /B). The structure in [16] is based on an internal memory data structure obtained independently by Arikati et al [7] and Djidjev [12] using planar separators and ideas due to Frederickson =-=[14, 15]-=-. In internal memory, this structure has been generalized to obtain a family of structures, such that a structure using S ∈ [N,N 2 ] space can answer shortest path distance queries in O(N 2 /S) time [... |

148 | Fast algorithms for shortest paths in planar graphs, with applications
- Frederickson
- 1987
(Show Context)
Citation Context ...ct is O(N 2 /B). The structure in [16] is based on an internal memory data structure obtained independently by Arikati et al [7] and Djidjev [12] using planar separators and ideas due to Frederickson =-=[14, 15]-=-. In internal memory, this structure has been generalized to obtain a family of structures, such that a structure using S ∈ [N,N 2 ] space can answer shortest path distance queries in O(N 2 /S) time [... |

75 | Improved Algorithms and Data Structures for Solving Graph
- Kumar, Schwabe
- 1996
(Show Context)
Citation Context ... for SSSP, as well the best algorithms for the simpler BFS and DFS problems, use Ω(|V |) I/Os.Moreprecisely, their I/O-complexity is O(min{(|V | + |E|/B) · log |V | +sort(|E|), |V | + |V | |E| M B }) =-=[8,11,17]-=- . However, improved algorithms have been developed for planar digraphs [5, 6,3]. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these alg... |

59 | On external memory graph traversal
- Buchsbaum, Goldwasser, et al.
- 2000
(Show Context)
Citation Context ... for SSSP, as well the best algorithms for the simpler BFS and DFS problems, use Ω(|V |) I/Os.Moreprecisely, their I/O-complexity is O(min{(|V | + |E|/B) · log |V | +sort(|E|), |V | + |V | |E| M B }) =-=[8,11,17]-=- . However, improved algorithms have been developed for planar digraphs [5, 6,3]. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these alg... |

44 | Planar spanners and approximate shortest path queries among obstades
- Arikati, Chen, et al.
- 1996
(Show Context)
Citation Context ... this paper we develop a family of structures with a trade-off between space use and the number of I/Os needed to answer a query. Although this problem has been extensively studied in internal memory =-=[7, 13, 12, 10, 9]-=-, this is the first result of its type in external memory. 1.1 I/O-Model and Related Work We will be working in the standard two-level I/O model [1], where M is the number of vertices that can fit int... |

32 | On external memory MST, SSSP and multiway planar graph separation
- Arge, Brodal, et al.
- 2000
(Show Context)
Citation Context ...loped for planar digraphs [5, 6,3]. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these algorithms are based on I/O-efficient reductions =-=[2,4,5,6]-=- and on an O(sort(N)) I/O planar graph separator algorithm [19]. 1 The planar separator algorithm [19] makes the stronger but realistic assumption that M>B 2 lg 2 B; we make this assumption indirectly... |

24 | On External-Memory Planar Depth First Search
- Arge, Meyer, et al.
- 2001
(Show Context)
Citation Context ...loped for planar digraphs [5, 6,3]. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these algorithms are based on I/O-efficient reductions =-=[2,4,5,6]-=- and on an O(sort(N)) I/O planar graph separator algorithm [19]. 1 The planar separator algorithm [19] makes the stronger but realistic assumption that M>B 2 lg 2 B; we make this assumption indirectly... |

16 |
I/O-Optimal Algorithms for Planar Graphs Using Separators
- Maheshwari, Zeh
- 2002
(Show Context)
Citation Context ... be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these algorithms are based on I/O-efficient reductions [2,4,5,6] and on an O(sort(N)) I/O planar graph separator algorithm =-=[19]-=-. 1 The planar separator algorithm [19] makes the stronger but realistic assumption that M>B 2 lg 2 B; we make this assumption indirectly as we rely on planar separators.s330 L. Arge and L. Toma The o... |

14 | Efficient algorithms for shortest path queries in planar digraphs
- Djidjev
- 1996
(Show Context)
Citation Context ... this paper we develop a family of structures with a trade-off between space use and the number of I/Os needed to answer a query. Although this problem has been extensively studied in internal memory =-=[7, 13, 12, 10, 9]-=-, this is the first result of its type in external memory. 1.1 I/O-Model and Related Work We will be working in the standard two-level I/O model [1], where M is the number of vertices that can fit int... |

13 |
Shortest path queries in digraphs of small treewidth
- Chaudhuri, Zaroliagis
(Show Context)
Citation Context ... this paper we develop a family of structures with a trade-off between space use and the number of I/Os needed to answer a query. Although this problem has been extensively studied in internal memory =-=[7, 13, 12, 10, 9]-=-, this is the first result of its type in external memory. 1.1 I/O-Model and Related Work We will be working in the standard two-level I/O model [1], where M is the number of vertices that can fit int... |

12 | Shortest path queries in planar graphs
- Chen, Xu
- 2000
(Show Context)
Citation Context |

11 | An externalmemory data structure for shortest path queries
- Hutchinson, Maheshwari, et al.
- 1999
(Show Context)
Citation Context ...tion indirectly as we rely on planar separators.s330 L. Arge and L. Toma The only known I/O-efficient external data structure for answering shortest path queries is a structure for planar digraphs in =-=[16]-=-. The structure uses O(N √ N) space and answers shortest path distance queries in O( √ N/B)I/Os (and can report the shortest path with additional O(K/B)I/Os,whereK is the number of edges on the path).... |

10 | I/O-efficient topological sorting of planar dags
- Arge, Toma, et al.
- 2003
(Show Context)
Citation Context ...Ω(|V |) I/Os.Moreprecisely, their I/O-complexity is O(min{(|V | + |E|/B) · log |V | +sort(|E|), |V | + |V | |E| M B }) [8,11,17] . However, improved algorithms have been developed for planar digraphs =-=[5, 6,3]-=-. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these algorithms are based on I/O-efficient reductions [2,4,5,6] and on an O(sort(N)) I/O... |

10 |
Computing shortest paths and distances in planar graphs
- Djidjev, Pantziou, et al.
- 1991
(Show Context)
Citation Context |

9 |
External Memory Algorithms for Diameter and All-Pairs Shortest-Paths on Sparse Graphs
- Arge, Meyer, et al.
- 2004
(Show Context)
Citation Context ...Ω(|V |) I/Os.Moreprecisely, their I/O-complexity is O(min{(|V | + |E|/B) · log |V | +sort(|E|), |V | + |V | |E| M B }) [8,11,17] . However, improved algorithms have been developed for planar digraphs =-=[5, 6,3]-=-. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these algorithms are based on I/O-efficient reductions [2,4,5,6] and on an O(sort(N)) I/O... |

8 | I/O-efficient strong connectivity and depth-first search for directed planar graphs
- Arge, Zeh
- 2003
(Show Context)
Citation Context ...Ω(|V |) I/Os.Moreprecisely, their I/O-complexity is O(min{(|V | + |E|/B) · log |V | +sort(|E|), |V | + |V | |E| M B }) [8,11,17] . However, improved algorithms have been developed for planar digraphs =-=[5, 6,3]-=-. On such graphs, SSSP and BFS can be solved in O(sort(N)) I/Os [5], and DFS in O(sort(N)logN/M) I/Os [6]; all these algorithms are based on I/O-efficient reductions [2,4,5,6] and on an O(sort(N)) I/O... |