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## Advanced Shortest Paths Algorithms on a Massively-Multithreaded Architecture

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Citations: | 4 - 0 self |

### Citations

1055 |
A Note Two Problems in Connection with Graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ...ntative distance value, d(v), for each v ∈ V . This value is updated by relaxing the edges out of a vertex v while visiting v. Relaxing an edge e = (u, v) sets d(v) = min(d(v), d(u) + ℓ(e)). Dijkstra =-=[6]-=- noted in his famous paper that the problem can be solved by visiting vertices in nondecreasing order of their d-values. Dijkstra’s algorithm maintains three sets of vertices: unreached, queued, and s... |

240 | R-mat: A recursive model for graph mining
- CHAKRABARTI, ZHAN, et al.
- 2004
(Show Context)
Citation Context ...first constructing a cycle, and then adding m − n edges to the graph at random. The generator may produce parallel edges as well as self-loops. • Scale-free graphs (RMAT): We use the R-MAT graph mode =-=[3]-=- to generate Scalefree instances. This algorithm recursively fills in an adjacency matrix in such a way that the distribution of vertex degrees obeys an inverse power law. For each of these graph clas... |

136 |
An O(log n) parallel connectivity algorithm
- Shiloach, Vishkin
- 1982
(Show Context)
Citation Context ...lgorithm, and we use the “bully algorithm” for connected components available in the MultiThreaded Graph Library (MTGL) [2]. This algorithm avoids hot spots inherent in the Shiloach-Vishkin algorithm =-=[14]-=- and demonstrates near-perfect scaling through 40 MTA-2 processors on the unstructured instances we study. 3.2. Run-time Data Structures We define minD(c) for component c as min(d(x)|x ∈ c\S). The val... |

121 |
Undirected Single-Source Shortest Paths with Positive Integer Weights in Linear Time
- Thorup
- 1999
(Show Context)
Citation Context ...nd an elegant computer architecture. Finally, we conclude with a prediction that this work will become relevant to shortest path computation on structured networks. 1. Introduction Thorup’s algorithm =-=[15]-=- solves the SSSP problem for undirected graphs with positive integer weights in linear time. To accomplish this, Thorup’s algorithm encapsulates 1-4244-0910-1/07/$20.00 c○2007 IEEE. 3 Georgia Institut... |

38 | A Simple Shortest Path Algorithm with Linear Average Time
- Goldberg
(Show Context)
Citation Context ...the “DIMACS reference solver,” an implementation of Goldberg’s multilevel bucket shortest path algorithm, which has an expected running time of O(n) on random graphs with uniform weight distributions =-=[7]-=-. We compare these two implementations to establish that our implementation is portable and that it does not perform much extra work. It is reasonable to compare these implementations because they ope... |

28 | Improved shortest paths on the word RAM
- Hagerup
(Show Context)
Citation Context ...by multiple concurrent SSSP computations. Thorup’s SSSP algorithm and the data structures that it uses are complex. The algorithm has been generalized to run on directed graphs in O(n + m log w) time =-=[8]-=- (where w is word-length in bits) and in the pointer-addition model of computation in O(mα(m, n) + n log log r) time [13] (where α(m, n) is Tarjan’s inverse-Ackermann function and r is the ratio of th... |

25 | Computing Many-to-Many Shortest Paths Using Highway Hierarchies
- Knopp, Sanders, et al.
- 2007
(Show Context)
Citation Context ...orks, prove to be very difficult for parallel delta stepping regardless of instance size. Finding shortest paths in these structured road network instances has become an active research area recently =-=[1, 9]-=-. When geographical information is available, precomputations to identify “transit nodes” [1] make subsequent s-t shortest path queries extremely fast. However, depending on the parameters of the algo... |

23 | Ramachandran V. Computing Shortest Paths with Comparisons and
- Pettie
(Show Context)
Citation Context ...algorithm has been generalized to run on directed graphs in O(n + m log w) time [8] (where w is word-length in bits) and in the pointer-addition model of computation in O(mα(m, n) + n log log r) time =-=[13]-=- (where α(m, n) is Tarjan’s inverse-Ackermann function and r is the ratio of the maximum-to-minimum edge length). In this paper, we perform an experimental study of Thorup’s original algorithm. In ord... |

17 |
transit to constant time shortest-path queries in road networks
- In
- 2007
(Show Context)
Citation Context ...orks, prove to be very difficult for parallel delta stepping regardless of instance size. Finding shortest paths in these structured road network instances has become an active research area recently =-=[1, 9]-=-. When geographical information is available, precomputations to identify “transit nodes” [1] make subsequent s-t shortest path queries extremely fast. However, depending on the parameters of the algo... |

16 | An experimental study of a parallel shortest path algorithm for solving large-scale graph instances
- Madduri, Bader, et al.
- 2007
(Show Context)
Citation Context ..., as they tend to be dominated by latency and to benefit little from cache. We are interested in leveraging such architectures to solve large shortest paths problems of various types. Madduri, et al. =-=[11]-=- demonstrate that for certain inputs, deltastepping [12], a parallel Dijkstra variant, can achieve relative speedups of roughly 30 in 40-processor runs on the MTA-2. This performance is achieved while... |

15 | Stepping : A Parallel Single Source Shortest Path Algorithm
- Meyer, Sanders
- 1998
(Show Context)
Citation Context ... little from cache. We are interested in leveraging such architectures to solve large shortest paths problems of various types. Madduri, et al. [11] demonstrate that for certain inputs, deltastepping =-=[12]-=-, a parallel Dijkstra variant, can achieve relative speedups of roughly 30 in 40-processor runs on the MTA-2. This performance is achieved while finding singlesource shortest paths on an unstructured ... |

14 | Parallel shortestpathalgorithmsforsolvinglarge-scaleinstances. In9th DIMACSImplementation Challenge
- Madduri, Bader, et al.
- 2006
(Show Context)
Citation Context ...e MTA-2 has support for primitive locking operations, as well as many other interesting features. An overview of the features is beyond the scope of this discussion, but is available as Appendix A of =-=[10]-=-. In addition to the MTA-2, our implementation compiles on sequential processors without modification. We used a Linux workstation to evaluate the sequential performance of our Thorup implementation. ... |

4 |
Graph software development and performance on the MTA-2 and Eldorado
- Berry, Hendrickson, et al.
- 2006
(Show Context)
Citation Context ...ion 3.2. Our implementation relies on repeated calls of a connected components algorithm, and we use the “bully algorithm” for connected components available in the MultiThreaded Graph Library (MTGL) =-=[2]-=-. This algorithm avoids hot spots inherent in the Shiloach-Vishkin algorithm [14] and demonstrates near-perfect scaling through 40 MTA-2 processors on the unstructured instances we study. 3.2. Run-tim... |

1 |
The XMT platform. http://www.cray. com/products/xmt
- Cray
- 2006
(Show Context)
Citation Context ...n of Thorup’s algorithm and detail the experimental setup. Finally, we present experimental results and plans for future work. 2. Background and Related Work The Cray MTA-2 and its successor, the XMT =-=[4]-=-, are massively multithreaded machines that provide elaborateshardware support for latency tolerance, as opposed to latency mitigation. Specifically, a large amount of chip space is devoted to support... |