Computation of a Tree 3-Spanner on Trapezoid Graphs

In a graph G , a spanning tree T is said to be a tree t-spanner of the graph G if the distance between any two vertices in T is at most t times their distance in G. The tree t-spanner has many applications in networks an d distributed environments. In this paper, an algorithm is presented to find a tree 3 -spanner on trapezoid graphs in ) ( 2 n O time, where n is the number of vertices of the graph.

[1]  Eli Upfal,et al.  A tradeoff between space and efficiency for routing tables , 1988, STOC '88.

[2]  N.R. Malik,et al.  Graph theory with applications to engineering and computer science , 1975, Proceedings of the IEEE.

[3]  Sajal K. Das,et al.  Breadth-First Traversal of Trees and Integer Sorting in Parallel , 1992, ICPP.

[4]  Baruch Awerbuch,et al.  Complexity of network synchronization , 1985, JACM.

[5]  Madhumangal Pal,et al.  Optimal Sequential and Parallel Algorithms to Compute All Cut Vertices on Trapezoid Graphs , 2004, Comput. Optim. Appl..

[6]  Madhumangal Pal,et al.  An Algorithm to find a Minimum Feedback Vertex Set of an Interval Graph , 2005 .

[7]  Madhumangal Pal,et al.  Selection of programme slots of television channels for giving advertisement: A graph theoretic approach , 2007, Inf. Sci..

[8]  Leizhen Cai,et al.  NP-Completeness of Minimum Spanner Problems , 1994, Discret. Appl. Math..

[9]  A. Dress,et al.  Reconstructing the shape of a tree from observed dissimilarity data , 1986 .

[10]  Madhumangal Pal,et al.  An efficient algorithm to generate all maximal independent sets on trapezoid graphs , 1999, Int. J. Comput. Math..

[11]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms (Working Paper) , 1971, SWAT.

[12]  Madhumangal Pal,et al.  An Optimal Algorithm to Find Maximum and Minimum Height Spanning Trees on Cactus Graphs , 2008 .

[13]  Madhumangal Pal,et al.  An Efficient Algorithm for Finding All Hinge Vertices on Trapezoid Graphs , 2002, Theory of Computing Systems.

[14]  C. Pandu Rangan,et al.  Restrictions of Minimum Spanner Problems , 1997, Inf. Comput..

[15]  Narsingh Deo,et al.  Graph Theory with Applications to Engineering and Computer Science , 1975, Networks.

[16]  Madhumangal Pal,et al.  An optimal parallel algorithm for computing cut vertices and blocks on interval graphs , 2000, Int. J. Comput. Math..

[17]  Leizhen Cai,et al.  Spanners in graphs of bounded degree , 1994, Networks.

[18]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[19]  C. Pandu Rangan,et al.  Tree 3-Spanners on Interval, Permutation and Regular Bipartite Graphs , 1996, Inf. Process. Lett..

[20]  Madhumangal Pal,et al.  An optimal parallel algorithm to construct a tree 3-spanner on interval graphs , 2005, Int. J. Comput. Math..

[21]  Madhumangal Pal,et al.  An efficient pram algorithm for maximum-weight independent set on permutation graphs , 2005 .

[22]  Ron Y. Pinter,et al.  Trapezoid graphs and their coloring , 1988, Discret. Appl. Math..

[23]  Madhumangal Pal,et al.  An Efficient Algorithm for Finding a Maximum Weight k-Independent Set on Trapezoid Graphs , 2001, Comput. Optim. Appl..

[24]  Madhumangal Pal,et al.  Maximum weight k-independent set problem on permutation graphs , 2003, Int. J. Comput. Math..

[25]  Madhumangal Pal,et al.  A sequential algorithm for finding a maximum weight K-independent set on interval graphs , 1996, Int. J. Comput. Math..

[26]  M. Pal,et al.  A Sequential Algorithm to Solve Next-to-Shortest Path Problem on Circular-arc Graphs , 2006 .

[27]  Madhumangal Pal,et al.  An Optimal Parallel Algorithm to Color an Interval Graph , 1996, Parallel Process. Lett..

[28]  Madhumangal Pal.  Efficient algorithms to compute all articulation points of a permutation graph , 1998 .

[29]  Madhumangal Pal,et al.  An Optimal Algorithm for Solving All-Pairs Shortest Paths on Trapezoid Graphs , 2002, Int. J. Comput. Eng. Sci..

[30]  M. Golummc.  Algorithmic graph theory and perfect graphs , 1980 .

[31]  Madhumangal Pal,et al.  An optimal pram algorithm for a spanning tree on trapezoid graphs , 2003 .

[32]  Y. Daniel Liang,et al.  Dominations in Trapezoid Graphs , 1994, Inf. Process. Lett..

[33]  David Peleg,et al.  An Optimal Synchronizer for the Hypercube , 1989, SIAM J. Comput..

[34]  Stefan Hougardy,et al.  Classes of perfect graphs , 2006, Discret. Math..

[35]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[36]  Madhumangal Pal,et al.  A linear time algorithm to construct a tree 4-spanner on trapezoid graphs , 2010, Int. J. Comput. Math..

[37]  Paul Chew,et al.  There is a planar graph almost as good as the complete graph , 1986, SCG '86.