Optimal Sequential And Parallel Algorithms To Compute A Steiner Tree On Permutation Graphs

This paper presents an optimal sequential and an optimal parallel algorithm to compute a minimum cardinality Steiner set and a Steiner tree. The sequential algorithm takes O ( n ) time and parallel algorithm takes O (log n ) time and O ( n /log n ) processors on an EREW PRAM model.

[1]  A. Lempel,et al.  Transitive Orientation of Graphs and Identification of Permutation Graphs , 1971, Canadian Journal of Mathematics.

[2]  Jeremy P. Spinrad,et al.  Incremental modular decomposition , 1989, JACM.

[3]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

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

[5]  Fang-Rong Hsu,et al.  An Optimal EREW Parallel Algorithm for Computing Breadth-First Search Trees on Permutation Graphs , 1997, Inf. Process. Lett..

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

[7]  Larry Rudolph,et al.  The power of parallel prefix , 1985, IEEE Transactions on Computers.

[8]  Martin Farber,et al.  Steiner trees, connected domination and strongly chordal graphs , 1985, Networks.

[9]  Charles J. Colbourn,et al.  Permutation graphs: Connected domination and Steiner trees , 1991, Discret. Math..

[10]  S. Lakshmivarahan,et al.  Efficient Algorithms for Finding Depth-First and Breadth-First Search Trees in Permutation Graphs , 1994, Inf. Process. Lett..

[11]  K. Arvind,et al.  Connected Domination and Steiner Set on Weighted Permutation Graphs , 1992, Inf. Process. Lett..

[12]  R. Möhring Algorithmic graph theory and perfect graphs , 1986 .

[13]  Marina Moscarini,et al.  Distance-Hereditary Graphs, Steiner Trees, and Connected Domination , 1988, SIAM J. Comput..

[14]  C. Pandu Rangan,et al.  Efficient Parallel Algorithms for Permutation Graphs , 1995, J. Parallel Distributed Comput..

[15]  S. Sitharama Iyengar,et al.  Introduction to parallel algorithms , 1998, Wiley series on parallel and distributed computing.

[16]  Hon-Chan Chen,et al.  An O(log n) Parallel Algorithm for Constructing a Spanning Tree on Permutation Graphs , 1995, Inf. Process. Lett..