Browse > Article
http://dx.doi.org/10.5391/JKIIS.2007.17.7.893

A Point-to-Point Shortest Path Search Algorithm for Digraph  

Lee, Sang-Un (강릉대학교 컴퓨터정보공학부 멀티미디어정보공학)
Publication Information
Journal of the Korean Institute of Intelligent Systems / v.17, no.7, 2007 , pp. 893-900 More about this Journal
Abstract
This paper suggests an algorithm that improves the disadvantages of the Dijkstra algorithm that is commonly used in GPS navigation system, searching for the shortest path. Dijkstra algorithm, first of all, requires much memory for the performance of the algorithm. It has to carry out number of node minus 1, since it determines the shortest path from all the nodes in the graph, starting from the first node. Therefore, Dijkstra algorithm might not be able to provide the information on every second, searching for the shortest path between the roads of the congested city and the destination. In order to solve these problems, this paper chooses a method of searching a number of nodes at once by means of choosing the shortest path of all the path nodes (select of minimum weight arc in-degree and out-degree), excluding the departure and destination nodes, and of choosing all the arcs that coincide with the shortest path of the path nodes, from all the node outgoing arcs starting from the departure node. On applying the suggested algorithm to 14 various digraphs, we succeeded to search the shortest path. In addition, the result was obtained at the speed of 2 to 3 times faster than that of Dijkstra algorithm, and the memory required was less than that of Dijkstra algorithm.
Keywords
Digraph or Directed Graph; Shortest Path; Dijkstra's Algorithm; Minimum-weight Arc; Point-to-Point Shortest Path Search;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. B. Orlin, 'Network Optimization: Dijkstra's Algorithm for the Shortest Path Problem,' http://www.mit.edu/~jorlin/15.082/Lectures/05Dijkstra.ppt, MIT, 2003
2 T. H. Cormen, C. E. Leserson, R. L. Rivest, and C. Stein, 'Introduction to Algorithms,' 2nd Edition, MIT Press and McGraw-Hill, 2001
3 O. Boruvka, 'O Jistem Problemu Minimalnim,' Prace Mor. Prrodved. Spol. V Brne (Acta Societ. Natur. Moravicae), Vol. III, No.3, pp. 37-58, 1926
4 R. Wenger, 'CIS 780: Analysis of Algorithms,' http://www.cse.ohio-state.edu/~wenger/cis780/shortest_path.pdf, 2004
5 S. Boyd, 'Applications of Combinational Optimization: Optimal Paths and Trees,' http://www.site.uottawa.ca/~sylvia/csi5166web/5166tespg26to61.pdf, School of Information Technology and Engineering (SITE), University of Ottawa, Canada, 2005
6 R. Coleman, 'CS 221: Data Structures,' Computer Science, University of Alabama in Huntsville, 2002
7 K. S. Lee, 'Shortest Path Algorithm' http://www.geocities.com/lekinsengl/
8 M. Abboud, L. Mariya, A. Jaoude, and Z. Kerbage, 'Real Time GPS Navigation System,' 3rd FEA Student Conference, Department of Electrical and Computer Engineering, American University of Beirut, 2004
9 J. Nesetril, E. Milkova, and H. Nesetrilova, 'Otakar Boruvka on Minimum Spanning Tree Problem (Translation of the both 1926 Papers, Comments, History),' DMATH: Discrete Mathematics, Vol. 233, 2001
10 WWL. Chen, 'Discrete Mathematics,' Department of Mathematics, Division of ICS, Macquarie University, Australia, http://www.maths.mq.edu.au/~wchen/lndmfolder/lndm.html, 2003
11 J. Misra, 'A Walk Over the Shortest Path: Dijkstra's Algorithm Viewed as Fixed-Point Computation,' Department of Computer Science, University of Texas at Austin, USA, 2000
12 Y. T. Lim and H. M. Kim, 'A Shortest Path Algorithm for Real Road Network Based on Path Overlap,' Department of Civil Engineering, Institute of Transportation Studies, University of California, Irvine, USA, http://www.its.uci.edu/hyunmyuk/library/ (2005) 20EAST(k-path).pdf, 2005
13 R. C. Prim, 'Shortest Connection Networks and Some Generalisations,' Bell System Technical Journal, Vol. 36, pp. 1389-1401, 1957   DOI
14 F. B. Zhan, 'Three Fatest Shortest Path Algorithms on Real Road Networks: Data Structures and Procedures,' Journal of Geographic Informaton and Decision Analysis, Vol. 1, No.1, pp. 69-82, 1997
15 D. Walker, 'COS 226: Algorithms and Data Structures,' Department of Computer Science, Princeton University, http://www.cs.princeton.edu/ courses/ archi ve/fall04/ cos226/lectures/ shortest-path.pdf, 2004
16 M. Llewellyn, 'COP 3503: Computer Science II Introduction to Graphs,' http://www.cs.ucf.edu/ courses/cop3503/ summer04, 2004
17 Wikipedia, 'Dijkstra's Algorithm,' http://en.wikipedia.org/wiki/Dijkstra_algorithm, Wikimedia Foundation Inc., 2007
18 E. W. Dijkstra, 'A Note on Two Problems in Connection with Graphs,' Numerische Mathematik, Vol. 1, pp. 269-271, 1959   DOI
19 K. Ikeda, 'Mathematical Programming,' Dept. Information Science and Intelligent Systems, The University of Tokushima, http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/maxflow/MaxflowApp. shtml. 2005