### Citations

1055 |
A Note Two Problems in Connection with Graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ...ost of the algorithms solving APSP problem aren’t universal and they show a good solution speed for graphs only with a certain set of properties. In particular, there are algorithms for sparse graphs =-=[6]-=-, for graphs with bounded integer edge weights [11] etc. Although the complexity of solving APSP gradually decreases with the invention of new algorithms, this approach for the search of metric charac... |

28 | HyperANF: Approximating the neighbourhood function of very large graphs on a budget
- Boldi, Rosa, et al.
- 2011
(Show Context)
Citation Context ...ces between graph vertices are searched with some degree of error allowing for reduction of computation time significantly. Among such, for example, is the Approximate neighborhood function algorithm =-=[2]-=- or [1]. Apart from the search of exact and approximate characteristics of a graph, the search for the so-called graph effective characteristics is widely spread. The effective radius of a vertex v is... |

9 | Determining the diameter of small world networks
- Takes, Kosters
- 2011
(Show Context)
Citation Context ...ric characteristics for graphs having a special organization and describing peculiar structures. Among these, for example, is the algorithm for finding of the diameter for Small World Networks graphs =-=[12]-=- or the algorithm for finding of the center and diameter for Benzenoid Systems’ graphs [4]. To increase the speed of a solution, these algorithms use peculiarities of the respective graphs, and theref... |

3 |
Introduction to Algorithms, Second Edition
- H, Rivest, et al.
- 2001
(Show Context)
Citation Context ...10 104 108 104 The proposed algorithms for Problem 1 (denoted by R1 and D1) have been compared to the a) Dijkstra algorithm performed for each vertex of graph in the implementation with a binary heap =-=[5]-=- for graphs with a small average vertex degree and b) to the Floyd-Warshall algorithm [7] for complete graphs (denoted by RC1 and DC1). As it is impossible within reasonable time to obtain the solutio... |

2 |
algorithms for all-pairs shortest paths in weighted graphs
- More
(Show Context)
Citation Context ...ng this task on weighted graphs with n vertices have a complexity from Õ(Cn2,376) for graphs with integer edge weights less than C [11] and up to O(n3/ log2 n) for graphs with arbitrary edge weights =-=[3]-=-. Obviously, the usage of these methods for structures consisting of hundreds of thousands to millions of vertices in many 1 cases is unsuitable or even practically unfeasible due to a large amount of... |

2 |
Algorithm 97: Shortest Path
- FloydR
(Show Context)
Citation Context ...pared to the a) Dijkstra algorithm performed for each vertex of graph in the implementation with a binary heap [5] for graphs with a small average vertex degree and b) to the Floyd-Warshall algorithm =-=[7]-=- for complete graphs (denoted by RC1 and DC1). As it is impossible within reasonable time to obtain the solution of the problem on high-dimensional graphs by using the Dijkstra algorithm, the running ... |

2 |
Efficient algorithms for shortest paths in sparse graph
- JohnsonD
(Show Context)
Citation Context ...h non-negative edge weights are considered since any graph without negativeweight cycles can be associated with the graph having only non-negative edge weights with preservation of the shortest paths =-=[8]-=-. In this paper, the algorithms for a quick search of metric characteristics of graphs for two problems mentioned above are presented. The main advantage of the proposed algorithms is that it is not n... |

1 |
Faster Approximation of Distances in Graphs // Algorithms and Data Structures
- BermanP
(Show Context)
Citation Context ...ween graph vertices are searched with some degree of error allowing for reduction of computation time significantly. Among such, for example, is the Approximate neighborhood function algorithm [2] or =-=[1]-=-. Apart from the search of exact and approximate characteristics of a graph, the search for the so-called graph effective characteristics is widely spread. The effective radius of a vertex v is the 90... |

1 |
and Diameter Problems in Plane Triangulations and Quadrangulations
- ChepoiV
(Show Context)
Citation Context ...ures. Among these, for example, is the algorithm for finding of the diameter for Small World Networks graphs [12] or the algorithm for finding of the center and diameter for Benzenoid Systems’ graphs =-=[4]-=-. To increase the speed of a solution, these algorithms use peculiarities of the respective graphs, and therefore the range of their effective application is rigidly restricted. One of the types of me... |

1 |
The Art Of Computer Programming Vol 1
- unknown authors
- 1997
(Show Context)
Citation Context ...e function of characteristics of its connected components (e.g., maximum), the problem can be reduced to the considered one by finding the connected components with the usage of fast existing methods =-=[9]-=-. Only graphs with non-negative edge weights are considered since any graph without negativeweight cycles can be associated with the graph having only non-negative edge weights with preservation of th... |

1 |
Radius Plots for Mining Tera-byte Scale Graphs: Algorithms
- Faloutsos, Leskovec
(Show Context)
Citation Context ...s from v. The effective diameter of a graph is the minimum distance within which 90% of all vertices are within reach of each other. Certain algorithms for such problems are proposed, for example, in =-=[10]-=-. A trivial method of solving Problem 2 is to examine the distances between all pairs of a graph vertices and determine those satisfying the definitions of the radius and diameter. The solving of this... |

1 |
Pairs Shortest Paths in Undirected Graphs with Integer Weights
- All
- 1999
(Show Context)
Citation Context ...itions of the center, radius and diameter. Known algorithms performing this task on weighted graphs with n vertices have a complexity from Õ(Cn2,376) for graphs with integer edge weights less than C =-=[11]-=- and up to O(n3/ log2 n) for graphs with arbitrary edge weights [3]. Obviously, the usage of these methods for structures consisting of hundreds of thousands to millions of vertices in many 1 cases is... |