#### DMCA

## Hierarchical Hub Labelings for Shortest Paths (2012)

### Cached

### Download Links

Venue: | PROCEEDINGS OF THE 20TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA’12), VOLUME 7501 OF LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 22 - 12 self |

### Citations

3321 |
Collective dynamics of ‘small-world’ networks
- Watts, Strogatz
- 1998
(Show Context)
Citation Context ...d by TDwc on various inputs: road networks [13], meshes [21], communication and collaboration networks [5], and artificial inputs (Delaunay triangulations, random geometric graphs, small-world graphs =-=[20, 22]-=-). For each graph, Table 1 shows its size (|V |), its density (|A|/|V |), the TDwc running time (time), the average resulting label size (La), and HL query time (qt). We then report the ratio of short... |

2384 | A note on two problems in connexion with graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ...nd smaller labels for road networks, improving the query speed. 1 Introduction Computing point-to-point shortest paths in a graph is a fundamental problem with many applications. Dijkstra’s algorithm =-=[14]-=- solves this problem in nearlinear time [18], but for some graph classes sublinear-time queries are possible if preprocessing is allowed (e.g., [12, 16]). In particular, Gavoille et al.’s distance lab... |

739 | Fibonacci heaps and their uses in improved network optimization algorithms
- Fredman, Tarjan
- 1987
(Show Context)
Citation Context ...v) + `(v, w) < d(w), we set d(w) = d(v) + `(v, w) and p(v) = w. The algorithm terminates when all vertices have been processed. Dijkstra’s worst-case running time, denoted by Dij(G), is O(m+ n log n) =-=[15]-=- in the comparison model, and even better in weaker models [18]. For some applications, even linear time is too slow. For faster queries, labeling algorithms preprocess the graph and store a label wit... |

285 |
Navigation in a small world
- Kleinberg
- 2000
(Show Context)
Citation Context ...d by TDwc on various inputs: road networks [13], meshes [21], communication and collaboration networks [5], and artificial inputs (Delaunay triangulations, random geometric graphs, small-world graphs =-=[20, 22]-=-). For each graph, Table 1 shows its size (|V |), its density (|A|/|V |), the TDwc running time (time), the average resulting label size (La), and HL query time (qt). We then report the ratio of short... |

148 | Reachability and distance queries via 2-hop labels.
- Cohen, Halperin, et al.
- 2003
(Show Context)
Citation Context ...th their distances to or from u. Labels obey the cover property : for any two vertices s and t, there exists a vertex w on the shortest s–t path that belongs to both labels (of s and t). Cohen at al. =-=[9]-=- give a polynomial-time algorithm to approximate the smallest labeling within a factor of O(log n), where n is the number of vertices. The average label size can be quite large (Ω( 3 √ n) even for pla... |

131 | Distance labeling in graphs.
- Gavoille, Peleg, et al.
- 2001
(Show Context)
Citation Context ...roblem with many applications. Dijkstra’s algorithm [14] solves this problem in nearlinear time [18], but for some graph classes sublinear-time queries are possible if preprocessing is allowed (e.g., =-=[12, 16]-=-). In particular, Gavoille et al.’s distance labeling algorithm [16] precomputes a label for each vertex such that the distance between any two vertices s and t can be computed given only their labels... |

82 | Engineering Route Planning Algorithms
- Delling, Sanders, et al.
- 2009
(Show Context)
Citation Context ...roblem with many applications. Dijkstra’s algorithm [14] solves this problem in nearlinear time [18], but for some graph classes sublinear-time queries are possible if preprocessing is allowed (e.g., =-=[12, 16]-=-). In particular, Gavoille et al.’s distance labeling algorithm [16] precomputes a label for each vertex such that the distance between any two vertices s and t can be computed given only their labels... |

60 | Combining Hierarchical and Goal-Directed SpeedUp Techniques for Dijkstra’s Algorithm.
- Bauer, Delling, et al.
- 2008
(Show Context)
Citation Context ...he one obtained by TDwc. Table 4. Performance of various algorithms. HL and CH preprocessing use 12 cores, others are sequential. prepro space query method [h:m] [GB] [µs] CH [17] 0:02 0.4 96.381 TNR =-=[7]-=- 0:58 3.7 1.775 TNR+AF [7] 2:00 5.7 0.992 HL local [2] 2:39 20.1 0.572 HL global [2] 2:45 21.3 0.276 HL-0 local 0:03 22.5 0.700 HL-15 local 0:05 18.8 0.556 HL-17 local 0:25 18.0 0.545 HL-∞ local 5:43 ... |

48 | R.F.: A hub-based labeling algorithm for shortest paths on road networks.
- Abraham, Delling, et al.
- 2011
(Show Context)
Citation Context ...s for road networks. Unfortunately, preprocessing algorithms with theoretical guarantees on the label size run in Ω(n4) time [9, 4, 1], which is impractical for all but small graphs. In previous work =-=[2]-=-, we showed how to compute labels for road networks based on contraction hierarchies (CH) [17], an existing preprocessing-based shortest path algorithm. The resulting labels are unexpectedly small [2]... |

44 | R.F.: Customizable route planning. - Delling, Goldberg, et al. - 2011 |

22 |
Exact Routing in Large Road Networks Using Contraction Hierarchies.
- Geisberger, Sanders, et al.
- 2012
(Show Context)
Citation Context ...he label size run in Ω(n4) time [9, 4, 1], which is impractical for all but small graphs. In previous work [2], we showed how to compute labels for road networks based on contraction hierarchies (CH) =-=[17]-=-, an existing preprocessing-based shortest path algorithm. The resulting labels are unexpectedly small [2], with average size 85 on a graph of Western Europe [13] with 18 million vertices. The corresp... |

19 | On-line exact shortest distance query processing
- Cheng, Yu
- 2009
(Show Context)
Citation Context ...number of vertices. The average label size can be quite large (Ω( 3 √ n) even for planar graphs [16]), but not always. On real-world DAG-like graphs, for instances, labels are quite small in practice =-=[8]-=-. Abraham et al. [4] conjecture that road networks have a small highway dimension, and show that if the highway dimension is polylogarithmic, so is the label size. This motivated the experimental stud... |

17 | A practical shortest path algorithm with linear expected time.
- Goldberg
- 2008
(Show Context)
Citation Context ...ng the query speed. 1 Introduction Computing point-to-point shortest paths in a graph is a fundamental problem with many applications. Dijkstra’s algorithm [14] solves this problem in nearlinear time =-=[18]-=-, but for some graph classes sublinear-time queries are possible if preprocessing is allowed (e.g., [12, 16]). In particular, Gavoille et al.’s distance labeling algorithm [16] precomputes a label for... |

17 | VC-Dimension and Shortest Path Algorithms
- Abraham, Delling, et al.
(Show Context)
Citation Context ...thmic, so is the label size. This motivated the experimental study of labels for road networks. Unfortunately, preprocessing algorithms with theoretical guarantees on the label size run in Ω(n4) time =-=[7, 3, 1]-=-, which is impractical for all but small graphs. In previous work [2], we showed how to compute labels for road networks based on contraction hierarchies (CH) [14], another preprocessing-based shortes... |

12 | Distributed time-dependent contraction hierarchies
- Kieritz, Luxen, et al.
- 2010
(Show Context)
Citation Context ...uery algorithm runs bidirectional Dijkstra on G+, but considers only upward arcs. The CH query performance and |A+| highly depend on the order in which vertices are shortcut. The best known orderings =-=[17, 19]-=- use online heuristics to estimate how “important” each vertex is based on local graph properties (such as the net number of shortcuts added if the vertex were contracted). The running time of CH prep... |

12 | Efficient traversal of mesh edges using adjacency primitives.
- Sander, Nehab, et al.
- 2008
(Show Context)
Citation Context ...{lev(v), lev(u) + 1}. We implement HL queries as in [2], with no compression unless mentioned otherwise. We first consider the orderings produced by TDwc on various inputs: road networks [13], meshes =-=[21]-=-, communication and collaboration networks [5], and artificial inputs (Delaunay triangulations, random geometric graphs, small-world graphs [20, 22]). For each graph, Table 1 shows its size (|V |), it... |

9 | Faster Batched Shortest Paths in Road Networks
- Delling, Goldberg, et al.
- 2011
(Show Context)
Citation Context ...r(v) < r(u) from Lb(u) analogously. The overall running time of this approach is O(nM3), since for each label we must run O(M2) queries, each in O(M) time. In practice, using the HL one-to-many query =-=[11]-=- may accelerate this approach. 7 Experiments We implemented CH, HL, and TD in C++ and compiled them with Visual C++ 2010, using OpenMP for parallelization. We use a 4-ary heap as priority queue. 8 The... |