Spanner Algorithm for Directed Graph Stream

被引：0
|
作者：
Zhang X. [1 ]
Li X. [1 ]
机构：
[1] College of Information, Liaoning University, Shenyang
来源：
Jisuanji Yanjiu yu Fazhan/Computer Research and Development | 2019年 / 56卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Cluster; Data stream; Directed graph; Spanner; Stretch factor;
D O I：
10.7544/issn1000-1239.2019.20170680
中图分类号：
学科分类号：
摘要：
With the rapid growth of analysis demand in many fields such as social network, transportation network, and bioinformatics network, the processing of large-scale graph data has become a new challenge of information technology. Graph spanner is a subgraph in which the distance between every pair of vertices falling into the given range defined by stretch factor. With the spanner, the storage and computational cost are reduced greatly for large-scale graph data processing. Most of existing research work focused on the spanner on undirected graph, and we propose an effective algorithm for directed graph spanner. Firstly, we re-define the concept of cluster set and three kinds of crucial edges including cluster edge, bridge edge and free edge, and analyze theoretically the correctness of (3,2)-spanner construction based on the crucial edges. Moreover, we propose a spanner algorithm for graph data in streaming model in which the edges is clustered and updated according to the type of end-point of edge, and then a (3,2)-spanner of full graph is constructed. Finally, we provide the theoretical analysis of space complexity O(n2/4), and present the experiments on the synthetic graph of power law model. Experiment results show our algorithm meet the definition of (3,2)-spanner, and has low time and space overhead. © 2019, Science Press. All right reserved.
引用
收藏
页码：655 / 665
页数：10
相关论文
共 23 条
  • [1] Dong R., Zhang X., Liu H., Et al., Representation and operations research of k<sup>2</sup>-MDD in large-scale graph data, Journal of Computer Research and Development, 52, 12, pp. 2783-2792, (2016)
  • [2] Baswana S., Kavitha T., Mehlhorn K., Et al., New constructions of (α, β)-spanners and purely additive spanners, Proc of the 16th ACM-SIAM Symp on Discrete Algorithms, pp. 672-681, (2005)
  • [3] Baswana S., Sen S., A simple linear time algorithm for computing (2k-1)-spanner of O(n<sup>1+1/k</sup>) size for weighted graphs, Proc of the 30th Int Conf on Automata, Languages and Programming, pp. 384-396, (2003)
  • [4] Roditty L., Thorup M., Zwick U., Deterministic constructions of approximate distance oracles and spanners, Proc of the 32nd Int Conf on Automata, Languages and Programming, pp. 261-272, (2005)
  • [5] Ausiello G., Franciosa P.G., Italiano G.F., Small stretch spanners on dynamic graphs, Journal of Graph Algorithms and Applications, 10, 2, pp. 365-385, (2005)
  • [6] Baswana S., Dynamic algorithms for graph spanners, Proc of the 14th European Symp on Algorithms, pp. 76-87, (2006)
  • [7] Gottlieb L.A., Roditty L., An optimal dynamic spanner for doubling metric spaces, Proc of the 16th European Symp on Algorithms, pp. 478-489, (2008)
  • [8] Feigenbaum J., Kannan S., Mcgregor A., Et al., Graph distances in the streaming model: The value of space, Proc of the 16th ACM-SIAM Symp on Discrete Algorithms, pp. 745-754, (2005)
  • [9] Baswana S., Faster streaming algorithms for graph apanners
  • [10] Ausiello G., Franciosa P.G., Italiano G.F., Small stretch (α, β)-spanners in the streaming model, Theoretical Computer Science, 410, 36, pp. 3406-3413, (2009)
123