JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Maximum Degree Vertex Central Located Algorithm for Bandwidth Minimization Problem
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Maximum Degree Vertex Central Located Algorithm for Bandwidth Minimization Problem
Lee, Sang-Un;
  PDF(new window)
 Abstract
The bandwidth minimization problem (BMP) has been classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. This paper suggests polynomial time heuristic algorithm is to find the solution of bandwidth minimization problem. To find the minimum bandwidth , for given graph G=(V,E), m=|V|,n=|E|, the proposed algorithm sets the maximum degree vertex in graph G into global central point (GCP), and labels the median value between [1,m] range. The graph G is partitioned into subgroup, the maximum degree vertex in each subgroup is set to local central point (LCP), and we adjust the label of LCP per each subgroup as possible as minimum distance from GCP. The proposed algorithm requires O(mn) time complexity for label to all of vertices. For various twelve graph, the proposed algorithm can be obtains the same result as known optimal solution. For one graph, the proposed algorithm can be improve on known solution.
 Keywords
Labeling;bandwidth;Maximum degree;Global central point;Local central point;
 Language
Korean
 Cited by
 References
1.
K. Varshney, "A New Evolutionary Algorithm with Level Node Swap for Bandwidth Minimization Problem," M. Sc., Mathematics, Dayalbagh Educational Institute, Agra, pp. 1-24, 2014.

2.
U. Feige, "Coping with the NP-Hardness of the Graph Bandwidth Problem," Lecture Notes in Computer Science, Vol. 1851, pp. 129-145, May 2000.

3.
C. Dubey, U. Feige, and W. Unger, "Hardness Results for Approximating the Bandwidth," Journal of Computer and System Sciences, Vol. 77, No. 1, pp. 62-90, Jan. 2010.

4.
T. Kojima and K. Ando, "Bandwidth of the Cartesian Product of Two Connected Graphs," Discrete Mathematics, Vol. 252, No. 1-3, pp. 227-235, May 2002. crossref(new window)

5.
P. Z. Chinn, J. Chvatalova, A. K. Dewdney, and N. E. Gibbs, "The Bandwidth Problem for Graphs and Matrices-A Survey," Journal of Graph Theory, Vol. 6, No. 3, pp. 223-254, Sep. 1982. crossref(new window)

6.
G. Hermann, "On Balanced Separators, Treewidth, and Cycle Rank," Journal of Combinatorics, Vol. 3, No. 4, pp. 669-682, Dec. 2012. crossref(new window)

7.
K. Haim and S. Ron, "Pathwidth, Bandwidth, and Completion Problems to Proper Interval Graphs with Small Cliques," SIAM Journal on Computing, Vol. 25, No. 3, pp. 540-561, Jun. 1996. crossref(new window)

8.
J. Diaz, J. Petit, and M. Serna, "A Survey of Graph Layout Problems," ACM Computing Surveys, Vol. 34, No. 3, pp. 313-356, Sep. 2002. crossref(new window)

9.
I. Safro, D. Ron and A. Brandt, "Multilevel Algorithms for Linear Ordering Problems," ACM Journal of Experimental Algorithmics, Vol. 13, pp. 1.4-1.20, 2009.

10.
C. M. Pintea, G. C. Crisan, and C. Chira, "A Hybrid ACO Approach to the Matrix Bandwidth Minimization Problem," Hybrid Artificial Intelligence Systems, Lecture Notes in Computer Science, Vol. 6076, pp. 405- 412, 2010.

11.
A. Esposito, M. S. Catalano, F. Malucelli, and L. Tarricone, "A New Matrix Bandwidth Reduction Algorithm," Operation Research Letters, Vol. 23, No. 3-5, pp. 99-107. Oct. 1998. crossref(new window)

12.
A. Lim, B. Rodrigues, and F. Xiao, "Using an Evolutionary Algorithm for Bandwidth Minimization," Congress on Evolutionary Computation, Vol. 1, pp. 678-683, Dec. 2003.

13.
A. Lim, B. Rodrigues, and F. Xiao, "Ant Colony Optimization and Hill Climbing for the Bandwidth Minimization Problem," Applied Software Computing, Vol. 6, No. 2, pp. 180-188, Jan. 2006. crossref(new window)

14.
A. Lim, J. Lin, and F. Xiao, "Particle Swarm Optimization and Hill Climbing to Solve the Bandwidth Minimization Problem," Applied Intelligence, Vol. 26, No. 3, pp. 175-182, Jun. 2007. crossref(new window)

15.
R. Marti, M. Laguna, F. Glover, and V. Campos, "Reducing the Bandwidth of a Sparse Matrix with Tabu Search," European Journal of Operational Research, Vol. 135, No. 2, pp. 450-459, Dec. 2001. crossref(new window)

16.
E. Pinana, I. Plana, V. Campos, and R. Marti, "GRASP and Path Relinking for the Matrix Bandwidth Minimization," European Journal of Operational Research, Vol. 153, No. 1, pp. 200-210, Feb. 2004. crossref(new window)

17.
F. R. K., Chung, "Graph Theory, Chap. 7: Labelings of Graphs," pp. 151-168, Academic Press, 1988.

18.
Z. Miller and J. B Orlin, "NP-Completeness for Minimizing Maximum Edge Length in Grid Embeddings," Journal of Algorithms, Vol. 6 No. 1, pp. 10-16, Mar. 1985. crossref(new window)