## Cache-oblivious planar shortest paths (2005)

Venue: | In Proc. 32nd International Colloquium on Automata, Languages, and Programming. LNCS |

Citations: | 3 - 1 self |

### BibTeX

@INPROCEEDINGS{Jampala05cache-obliviousplanar,

author = {Hema Jampala and Norbert Zeh},

title = {Cache-oblivious planar shortest paths},

booktitle = {In Proc. 32nd International Colloquium on Automata, Languages, and Programming. LNCS},

year = {2005},

pages = {563--575},

publisher = {Springer}

}

### OpenURL

### Abstract

Abstract. We present an efficient cache-oblivious implementation of the shortest-path algorithm for planar graphs by Klein et al., and prove that it incurs no more than O ` N B1/2−ɛ + N B log N ´ block transfers on a graph with N vertices. This is the first cache-oblivious algorithm for this problem that incurs o(N) block transfers. 1

### Citations

9301 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2009
(Show Context)
Citation Context ...unning time of the algorithm, which is often the case in large-scale applications. Complexities that arise often in I/O-efficient algorithms are the sorting bound, sort(N) = Θ ( N B logM/B N ) B I/Os =-=[1, 18]-=-, the permutation bound, perm(N) = Θ(min(N, sort(N))) I/Os [1], and the scanning bound, scan(N) = Θ(N/B) I/Os. Solving interesting problems using cache-aware algorithms for multi-level hierarchies is ... |

922 |
A note on two problems in connection with graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ... d(v) from s to v, that is, the weight of a minimum-weight (shortest) path from s to v. This problem is well-studied in the RAM-model. The classical algorithm for this problem is Dijkstra’s algorithm =-=[15]-=-, which has seen many improvements (e.g.,[19, 21–23]). In particular, on planar graphs, much progress has been made: Frederickson [17] proposes an algorithm that takes O(N √ log N) time, pioneering th... |

575 |
The input/output complexity of sorting and related problems
- Aggarwal, Vitter
- 1988
(Show Context)
Citation Context ... paging algorithm by laying out the data appropriately and accessing it in a local fashion. The most widely used model for the design of cache-aware algorithms is the I/O-model of Aggarwal and Vitter =-=[1]-=-. This model assumes a memory hierarchy consisting of two levels: the lower level has size M; data is transferred between the two levels in blocks of B consecutive data items. The complexity ⋆ Researc... |

183 | External-memory graph algorithms
- Chiang, Goodrich, et al.
- 1995
(Show Context)
Citation Context ... modelling, and data mining of phone call databases. The obtained results include a large number of algorithms for planar graphs, such as O(sort(N))- I/O algorithms for computing connected components =-=[13]-=-, minimum spanning trees [13], and strongly connected components [8]; breadth-first search (BFS) [3] and undirected depth-first search (DFS) [5]; single-source shortest paths [3]; and topological sort... |

171 | M.: Faster shortestpath algorithms for planar graphs
- Subramanian, Klein, et al.
- 1994
(Show Context)
Citation Context ...h progress has been made: Frederickson [17] proposes an algorithm that takes O(N √ log N) time, pioneering the idea to use separator decompositions to speed up shortestpath computations. Klein et al. =-=[19]-=- present a non-trivial refinement of Frederickson’s approach that uses a hierarchy of nested separator decompositions to solve SSSP in planar directed graphs in linear time. More recently, the SSSP-pr... |

126 |
Fast algorithms for shortest paths in planar graphs, with applications
- Frederickson
- 1987
(Show Context)
Citation Context ... The classical algorithm for this problem is Dijkstra’s algorithm [15], which has seen many improvements (e.g.,[19, 21–23]). In particular, on planar graphs, much progress has been made: Frederickson =-=[17]-=- proposes an algorithm that takes O(N √ log N) time, pioneering the idea to use separator decompositions to speed up shortestpath computations. Klein et al. [19] present a non-trivial refinement of Fr... |

71 | Cacheoblivious priority queue and graph algorithm applications
- Arge, Bender, et al.
- 2002
(Show Context)
Citation Context ...m is presented in [4]. Recently, a number of cache-oblivious graph algorithms have been obtained for general graphs, including algorithms for computing connected components and minimum spanning trees =-=[2]-=-, directed breadth-first search and depth-first search [2], undirected breadth-first search [12], and undirected shortest paths [12, 14]. All these algorithms are obtained from I/O-efficient algorithm... |

53 | Planar graphs, negative weight edges, shortest paths, and near linear time
- Fakcharoenphol, Rao
- 2001
(Show Context)
Citation Context ...by leading to an excessive number of block transfers. The internal-memory computation can often be reduced. For example, for shortest paths, it can be reduced to O(n · polylog(B)), using results from =-=[16]-=-; but these algorithms are not easily made cache-oblivious. Nevertheless, a number of cache-oblivious algorithms for planar graphs exist. Using cache-oblivious data structures from [2, 10], the I/O-ef... |

50 | Undirected single source shortest paths with positive integer weights in linear time - Thorup - 1999 |

44 | R.: Cache oblivious distribution sweeping
- Brodal, Fagerberg
- 2002
(Show Context)
Citation Context ...Thus, the cache-oblivious model elegantly combines the simplicity of the I/O-model with a coverage of the entire memory hierarchy. The bounds for sorting and scanning are the same as in the I/O-model =-=[9, 18]-=-, whereas perm(N) = sort(N) in the cache-oblivious model [11]. Since any internal-memory algorithm is by definition cache-oblivious, but usually incurs a substantial number of block transfers, we refe... |

41 | On the limits of cache-obliviousness
- Brodal, Fagerberg
- 2003
(Show Context)
Citation Context ...y of the I/O-model with a coverage of the entire memory hierarchy. The bounds for sorting and scanning are the same as in the I/O-model [9, 18], whereas perm(N) = sort(N) in the cache-oblivious model =-=[11]-=-. Since any internal-memory algorithm is by definition cache-oblivious, but usually incurs a substantial number of block transfers, we refer to an algorithm as cache-oblivious in this paper if it is c... |

26 | On external-memory MST, SSSP and multi-way planar graph separation
- Arge, Brodal, et al.
- 2000
(Show Context)
Citation Context ...lgorithms for planar graphs, such as O(sort(N))- I/O algorithms for computing connected components [13], minimum spanning trees [13], and strongly connected components [8]; breadth-first search (BFS) =-=[3]-=- and undirected depth-first search (DFS) [5]; single-source shortest paths [3]; and topological sorting [6, 7]. Directed planar DFS is studied in [8], and an optimal O(N 2 /B)-I/O all-pairs shortest p... |

26 | Cache-oblivious data structures and algorithms for undirected breadth-first search and shortest paths
- BRODAL, FAGERBERG, et al.
- 2004
(Show Context)
Citation Context ...d for general graphs, including algorithms for computing connected components and minimum spanning trees [2], directed breadth-first search and depth-first search [2], undirected breadth-first search =-=[12]-=-, and undirected shortest paths [12, 14]. All these algorithms are obtained from I/O-efficient algorithms for these problems by designing cache-oblivious data structures that can replace the cacheawar... |

25 | On external-memory planar depth first search
- Arge, Meyer, et al.
- 2001
(Show Context)
Citation Context ...N))- I/O algorithms for computing connected components [13], minimum spanning trees [13], and strongly connected components [8]; breadth-first search (BFS) [3] and undirected depth-first search (DFS) =-=[5]-=-; single-source shortest paths [3]; and topological sorting [6, 7]. Directed planar DFS is studied in [8], and an optimal O(N 2 /B)-I/O all-pairs shortest path algorithm is presented in [4]. Recently,... |

21 | Computing shortest paths with comparisons and additions - Pettie, Ramachandran |

19 |
I/O-optimal algorithms for planar graphs using separators
- Maheshwari, Zeh
(Show Context)
Citation Context ... (3) Can the O ( N B log N) -term be reduced to O(N/B) (the equivalent of the linear time bound obtained in [19]). To answer question (1), we believe that the contraction-based separator algorithm of =-=[20]-=- can be extended to compute the desired partition: At every contraction level, use the (by a constant factor suboptimal) separator produced at the previous level to compute a BFS-tree of the current l... |

18 | Floats, integers, and single source shortest paths - Thorup |

12 | Cache-oblivious shortest paths in graphs using buffer heap
- CHOWDHURY, RAMACHANDRAN
(Show Context)
Citation Context ...rithms for computing connected components and minimum spanning trees [2], directed breadth-first search and depth-first search [2], undirected breadth-first search [12], and undirected shortest paths =-=[12, 14]-=-. All these algorithms are obtained from I/O-efficient algorithms for these problems by designing cache-oblivious data structures that can replace the cacheaware ones in these algorithms. This strateg... |

8 |
External memory algorithms for diameter and all-pairs shortest-paths on sparse graphs
- Arge, Meyer, et al.
- 2004
(Show Context)
Citation Context ...arch (DFS) [5]; single-source shortest paths [3]; and topological sorting [6, 7]. Directed planar DFS is studied in [8], and an optimal O(N 2 /B)-I/O all-pairs shortest path algorithm is presented in =-=[4]-=-. Recently, a number of cache-oblivious graph algorithms have been obtained for general graphs, including algorithms for computing connected components and minimum spanning trees [2], directed breadth... |

8 | I/O-efficient strong connectivity and depth-first search for directed planar graphs
- Arge, Zeh
- 2003
(Show Context)
Citation Context ...ults include a large number of algorithms for planar graphs, such as O(sort(N))- I/O algorithms for computing connected components [13], minimum spanning trees [13], and strongly connected components =-=[8]-=-; breadth-first search (BFS) [3] and undirected depth-first search (DFS) [5]; single-source shortest paths [3]; and topological sorting [6, 7]. Directed planar DFS is studied in [8], and an optimal O(... |

6 |
I/O-efficient algorithms for planar digraphs
- Arge, Toma, et al.
- 2003
(Show Context)
Citation Context ...nimum spanning trees [13], and strongly connected components [8]; breadth-first search (BFS) [3] and undirected depth-first search (DFS) [5]; single-source shortest paths [3]; and topological sorting =-=[6, 7]-=-. Directed planar DFS is studied in [8], and an optimal O(N 2 /B)-I/O all-pairs shortest path algorithm is presented in [4]. Recently, a number of cache-oblivious graph algorithms have been obtained f... |

5 | Simplified external memory algorithms for planar DAGs
- Arge, Toma
- 2004
(Show Context)
Citation Context ...nimum spanning trees [13], and strongly connected components [8]; breadth-first search (BFS) [3] and undirected depth-first search (DFS) [5]; single-source shortest paths [3]; and topological sorting =-=[6, 7]-=-. Directed planar DFS is studied in [8], and an optimal O(N 2 /B)-I/O all-pairs shortest path algorithm is presented in [4]. Recently, a number of cache-oblivious graph algorithms have been obtained f... |

3 |
Funnel heap—a cache oblivious priority queue, in
- Brodal, Fagerberg
(Show Context)
Citation Context ...g results from [16]; but these algorithms are not easily made cache-oblivious. Nevertheless, a number of cache-oblivious algorithms for planar graphs exist. Using cache-oblivious data structures from =-=[2, 10]-=-, the I/O-efficient algorithms for connectivity, biconnectivity, and minimum spanning trees [13], and for topologically sorting planar directed acyclic graphs [7] can be made cache-oblivious, without ... |