## Examiner

### Abstract

by

### Citations

2532 | The Design and Analysis of Computer Algorithms - AHO, HOPCROFT, et al. - 1974 |

1582 | A note on two problems in connexion with graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ...w for all vertices in G. The single pair shortest path problem is to find the shortest path from one assigned vertex v to another assigned vertex w in G. For unrestricted graphs, Dijkstra’s algorithm =-=[9]-=- is still the most efficient algorithm for the SSSP problem. When Dijkstra’s algorithm uses an efficient data structure, such as Fibonacci heaps [10] or 2-3 heaps [24] in its priority queue manipulati... |

1166 |
C.: Algorithmic graph theory and perfect graphs (2nd
- Golumbic
- 2004
(Show Context)
Citation Context ...umed to consume a constant amount of computing time [21, 16]. 2.3 Graph Data Structures There are two data structures commonly used to represent a graph, namely adjacency matrices and adjacency lists =-=[14]-=-. An adjacency matrix for a digraph G = (V, E) with n vertices is an n × n matrix M: M(i, j) = 1 if (i, j) ∈ E = 0 otherwise Obviously, M is generally asymmetric since G is a digraph, and a spec11ifi... |

593 |
Fibonacci heaps and their uses in improved network optimization algorithms
- Fredman, Tarjan
- 1987
(Show Context)
Citation Context ...in G. For unrestricted graphs, Dijkstra’s algorithm [9] is still the most efficient algorithm for the SSSP problem. When Dijkstra’s algorithm uses an efficient data structure, such as Fibonacci heaps =-=[10]-=- or 2-3 heaps [24] in its priority queue manipulations, it can achieve O(m+nlogn) time where n is the number of vertices, and m is the number of edges of a given graph. We assume that the SSSP algorit... |

393 |
Introduction to Algorithms, 2nd ed
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...ld efficiently solve the APSP problem on dense graphs. As we said earlier, Dijkstra’s algorithm only works for graphs with non-negative edge weights, but the Bellman-Ford’s algorithm 18(described in =-=[7]-=-) allows graphs to have negative edge weights. In Dijkstra’s algorithm (see Algorithm 2.4), there are three sets, S, F and V − S − F , called a solution set, the frontier set and the unknown world res... |

264 |
Algorithmic Graph Theory
- Gibbons
- 1985
(Show Context)
Citation Context ...ay that e is incident with v. If there is an edge (v, w) ∈ E, v ∈ V and w ∈ V , then v is said to be adjacent to w. The degree of a vertex v, written degree(v), is the number of edges incident with v =-=[6]-=-. In Graph 1, degree(1) = 3, degree(2) = 2, degree(3) = 2, degree(4) = 3. A sub-graph of G is a graph obtained by removing some edges and/or vertices from G. The removal of a vertex will remove every ... |

20 | Shortest path algorithms: Engineering aspects, in - Goldberg |

7 | Are Fibonacci heaps optimal - Abuaiadh, Kingston |

7 |
On the shortest route through a network, Management Sci
- Dantzig
- 1960
(Show Context)
Citation Context ...ike New York, or a communication network with a large amount of connections like the Internet, then we will need more advanced technology to solve the shortest path problem instead of human intuition =-=[8]-=-. People use graphs to model problems of the real world. A graph is defined by a set of vertices and a set of edges that connect these vertices (see Figure 1.1). Therefore, to interpret a transport sy... |

4 | An efficient algorithm for the shortest path problem
- Abuaiadh, Kingston
- 1993
(Show Context)
Citation Context ...derlying graph structure, and always involves n delete-min operations. In order to efficiently compute the shortest paths for nearly acyclic graphs, several specialized algorithms have been published =-=[1, 3, 23, 20, 22]-=-. These works have shown that we can reduce the number of delete-min operations performed in priority queue manipulations. However, those specialized algorithms are based on two different measures of ... |

3 | Efficient shortest path algorithms by graph decomposition
- Abuaiadh, Kingston
- 1994
(Show Context)
Citation Context ...derlying graph structure, and always involves n delete-min operations. In order to efficiently compute the shortest paths for nearly acyclic graphs, several specialized algorithms have been published =-=[1, 3, 23, 20, 22]-=-. These works have shown that we can reduce the number of delete-min operations performed in priority queue manipulations. However, those specialized algorithms are based on two different measures of ... |

1 |
Fast algorithm for shortest path in planar graph, with applications
- Greg
- 1987
(Show Context)
Citation Context ...r 2-3 heaps for their priority queue manipulations. However, for restricted digraphs, we have efficient alternatives, like acyclic graphs with O(m+n) time [26] and planar graphs with O(n √ logn) time =-=[12]-=-. If a graph is nearly acyclic, obviously we should not use the conventional algorithms for general graphs. If we use Dijkstra’s algorithm, it does not count the underlying graph structure, and always... |