In most network analysis tools the computation of the shortest paths between all pairs of nodes is a fundamental step to the discovery of other properties. Among other properties is the computation of closeness centra...In most network analysis tools the computation of the shortest paths between all pairs of nodes is a fundamental step to the discovery of other properties. Among other properties is the computation of closeness centrality, a measure of the nodes that shows how central a vertex is on a given network. In this paper, the authors present a method to compute the All Pairs Shortest Paths on graphs that present two characteristics： abundance of nodes with degree value one, and existence of articulation points along the graph. These characteristics are present in many real life networks especially in networks that show a power law degree distribution as is the case of biological networks. The authors＇ method compacts the single nodes to their source, and then by using the network articulation points it disconnects the network and computes the shortest paths in the biconnected components. At the final step the authors proposed methods merges the results to provide the whole network shortest paths. The authors＇ method achieves remarkable speedup compared to state of the art methods to compute the shortest paths, as much as 7 fold speed up in artificial graphs and 3.25 fold speed up in real application graphs. The authors＇ performance improvement is unlike previous research as it does not involve elaborated setups since the authors algorithm can process significant instances on a popular workstation.展开更多
Bidirectional Dijkstra algorithm whose time complexity is 8O(n~2) is proposed. The theory foundation is that the classical Dijkstra algorithm has not any directional feature during searching the shortest path. The alg...Bidirectional Dijkstra algorithm whose time complexity is 8O(n~2) is proposed. The theory foundation is that the classical Dijkstra algorithm has not any directional feature during searching the shortest path. The algorithm takes advantage of the adjacent link and the mechanism of bidirectional search, that is, the algorithm processes the positive search from start point to destination point and the negative search from destination point to start point at the same time. Finally, combining with the practical application of route-planning algorithm in embedded real-time vehicle navigation system (ERTVNS), one example of its practical applications is given, analysis in theory and the experimental results show that compared with the Dijkstra algorithm, the new algorithm can reduce time complexity, and guarantee the searching precision, it satisfies the needs of ERTVNS.展开更多
Based on the definition of class shortest path in weighted rough graph, class shortest path algorithm in weighted rough graph is presented, which extends classical shortest path algorithm. The application in relations...Based on the definition of class shortest path in weighted rough graph, class shortest path algorithm in weighted rough graph is presented, which extends classical shortest path algorithm. The application in relationship mining shows effectiveness of it.展开更多
文摘In most network analysis tools the computation of the shortest paths between all pairs of nodes is a fundamental step to the discovery of other properties. Among other properties is the computation of closeness centrality, a measure of the nodes that shows how central a vertex is on a given network. In this paper, the authors present a method to compute the All Pairs Shortest Paths on graphs that present two characteristics： abundance of nodes with degree value one, and existence of articulation points along the graph. These characteristics are present in many real life networks especially in networks that show a power law degree distribution as is the case of biological networks. The authors＇ method compacts the single nodes to their source, and then by using the network articulation points it disconnects the network and computes the shortest paths in the biconnected components. At the final step the authors proposed methods merges the results to provide the whole network shortest paths. The authors＇ method achieves remarkable speedup compared to state of the art methods to compute the shortest paths, as much as 7 fold speed up in artificial graphs and 3.25 fold speed up in real application graphs. The authors＇ performance improvement is unlike previous research as it does not involve elaborated setups since the authors algorithm can process significant instances on a popular workstation.
文摘Bidirectional Dijkstra algorithm whose time complexity is 8O(n~2) is proposed. The theory foundation is that the classical Dijkstra algorithm has not any directional feature during searching the shortest path. The algorithm takes advantage of the adjacent link and the mechanism of bidirectional search, that is, the algorithm processes the positive search from start point to destination point and the negative search from destination point to start point at the same time. Finally, combining with the practical application of route-planning algorithm in embedded real-time vehicle navigation system (ERTVNS), one example of its practical applications is given, analysis in theory and the experimental results show that compared with the Dijkstra algorithm, the new algorithm can reduce time complexity, and guarantee the searching precision, it satisfies the needs of ERTVNS.
基金Natural Science Foundation of Shandong Province of China (Y2004A04)Natural Science Foundation of Shandong Province of China (Y2006A12)Foundation of Ministry of Fujian Province Education of China (JA04268).
文摘Based on the definition of class shortest path in weighted rough graph, class shortest path algorithm in weighted rough graph is presented, which extends classical shortest path algorithm. The application in relationship mining shows effectiveness of it.
