AN OPTIMAL ALGORITHM FOR SOLVING ALL-PAIRS SHORTEST PATHS ON TRAPEZOID GRAPHS

Abstract

International Journal of Computational Engineering ScienceVol. 03, No. 02, pp. 103-116 (2002) No AccessAN OPTIMAL ALGORITHM FOR SOLVING ALL-PAIRS SHORTEST PATHS ON TRAPEZOID GRAPHSSUKUMAR MONDAL, MADHUMANGAL PAL, and TAPAN K. PALSUKUMAR MONDALDepartment of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721 102, West Bengal, India Search for more papers by this author , MADHUMANGAL PALDepartment of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721 102, West Bengal, India Search for more papers by this author , and TAPAN K. PALDepartment of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721 102, West Bengal, India Search for more papers by this author https://doi.org/10.1142/S1465876302000575Cited by:14 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The Shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one node to another often gives the best way to route message between the nodes. This paper presents an O(n2) time algorithm for solving all pairs shortest path problems on trapezoid graphs which are extensions of interval graphs and permutation graphs. The space complexity of this algorithm is of O(n2). This problem has been solved by constructing n breadth-first search (BFS) trees with each of the n vertices as root. As the lower bound of time complexity for computing the all pairs shortest paths is known to be of O(n2), this proposed algorithm is optimal.Keywords:Design of algorithmsanalysis of algorithmsbreadth-first searchshortest-pathstrapezoid graph FiguresReferencesRelatedDetailsCited By 14Computation of diameter, radius and center of permutation graphsShaoli Nandi, Sukumar Mondal, and Sambhu Charan Barman6 December 2021 | Discrete Mathematics, Algorithms and Applications, Vol. 14, No. 08An optimal algorithm to find minimum k-hop connected dominating set of permutation graphsAmita Samanta Adhya, Sukumar Mondal, and Sambhu Charan Barman25 March 2020 | Asian-European Journal of Mathematics, Vol. 14, No. 04An Introduction to Intersection GraphsMadhumangal Pal1 Jan 2020Computation of Inverse 1-Center Location Problem on the Weighted Trapezoid GraphsBiswanath Jana, Sukumar Mondal and Madhumangal Pal1 May 2019 | Missouri Journal of Mathematical Sciences, Vol. 31, No. 1An optimal algorithm to find minimum k-hop dominating set of interval graphsSambhu Charan Barman, Madhumangal Pal, and Sukumar Mondal24 April 2019 | Discrete Mathematics, Algorithms and Applications, Vol. 11, No. 02Surjective L (2, 1)-labeling of cycles and circular-arc graphsSk. Amanathulla and Madhumangal Pal27 Jul 2018 | Journal of Intelligent & Fuzzy Systems, Vol. 35, No. 1L(0, 1)-Labelling of Trapezoid GraphsSatyabrata Paul, Madhumangal Pal and Anita Pal8 June 2017 | International Journal of Applied and Computational Mathematics, Vol. 3, No. S1Scheduling Algorithm to Select Optimal Programme Slots in Television Channels: A Graph Theoretic ApproachMadhumangal Pal and Anita Pal20 July 2016 | International Journal of Applied and Computational Mathematics, Vol. 3, No. 3Unrestricted and complete Breadth-First Search of trapezoid graphs in timeChristophe Crespelle and Philippe Gambette1 Jun 2010 | Information Processing Letters, Vol. 110, No. 12-13A linear time algorithm to construct a tree 4-spanner on trapezoid graphsSambhu Charan Barman, Sukumar Mondal and Madhumangal Pal1 Mar 2010 | International Journal of Computer Mathematics, Vol. 87, No. 4Counting the number of vertex covers in a trapezoid graphMin-Sheng Lin and Yung-Jui Chen1 Oct 2009 | Information Processing Letters, Vol. 109, No. 21-22An efficient algorithm to find next-to-shortest path on permutation graphsSambhu Charan Barman, Sukumar Mondal and Madhumangal Pal11 December 2008 | Journal of Applied Mathematics and Computing, Vol. 31, No. 1-2Efficient algorithms for the minimum connected domination on trapezoid graphsYin-Te Tsai, Yaw-Ling Lin and F.R. Hsu1 Jun 2007 | Information Sciences, Vol. 177, No. 12An optimal parallel algorithm for solving all-pairs shortest paths problem on circular-arc graphsAnita Saha, Madhumangal Pal and Tapan K. Pal1 Mar 2005 | Journal of Applied Mathematics and Computing, Vol. 17, No. 1-2 Recommended Vol. 03, No. 02 Metrics History KeywordsDesign of algorithmsanalysis of algorithmsbreadth-first searchshortest-pathstrapezoid graphPDF download