An efficient parallel algorithm for the efficient domination problem on distance-hereditary graphs

IEEE Transactions on Parallel and Distributed Systems

Volumn 13, Issue 9, 2002, Pages 985-993

  Hsieh, Sun Yuan ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

Binary tree contraction technique; Distance hereditary graphs; Parallel algorithm; PRAM; The efficient domination problem

Indexed keywords

COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; GRAPH THEORY; OPTIMIZATION; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING; RANDOM ACCESS STORAGE;

BINARY TREE CONTRACTION TECHNIQUE; DISTANCE HEREDITARY GRAPHS; SEQUENTIAL ALGORITHM;

PARALLEL ALGORITHMS;

EID: 0036766325     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPDS.2002.1036071     Document Type: Article

References (33)

1. K. Abrahamson, N. Dadoun, D.G. Kirkpatrick, and T. Przytycka, "A Simple Parallel Tree Contraction Algorithm," J. Algorithms, vol. 10, pp. 287-302, 1989.
2. H.J. Bandelt and H.M. Mulder, "Distance-Hereditary Graphs," J. Combinatorial Theory Series B, vol. 41, no. 1, pp. 182-208, 1989.
3. H.J. Bandelt, A. Henkmann, and F. Nicolai, "Powers of Distance-Hereditary Graphs," Discrete Math., vol. 145, pp. 37-60, 1995.
4. D. Bange, A. Barkauskas, and P. J. Slater, "Disjoint Dominating Sets in Trees," Sandia Laboratories Report, SAND 78-1087J, 1978.
5. D. Bange, A. Barkauskas, and P.J. Slater, "Efficient Dominating Sets in Graphs," Application of Discrete Math., R.D. Ringeisen and F.S. Roberts, Eds., pp. 189-199, 1988.
6. N. Biggs, "Perfect Codes in Graphs," J. Combinatorial Theory Series B, vol. 15, pp. 289-296, 1973.
7. A. Brandstädt and F.F. Dragan, "A Linear Time Algorithm for Connected γ-Domination and Steiner Tree on Distance-Hereditary Graphs," Networks, vol. 31, pp. 177-182, 1998.
8. M.S. Chang, and Y.C. Liu, "Polynomial Algorithm for the Weighted Perfect Domination Problems on Chordal Graphs and Split Graphs," Information Processing Letters, vol. 48, pp. 205-210, 1993.
9. G.J. Chang, C.P. Rangan, and S.R. Coorg, "Weighted Independent Perfect Domination on Cocomparability Graphs," Discrete Applied Math., vol. 63, pp. 215-222, 1995.
10. M.S. Chang, S.Y. Hsieh, and G.H. Chen, "Dynamic Programming on Distance-Hereditary Graphs," Proc. Seventh Int'l Symp. Algorithms and Computation (ISAAC'97), pp. 344-353, 1997.
11. Y.D. Liang, C.L. Lu, and C.Y. Tang, "Efficient Domination on Permutation Graphs and Trapezoid Graphs," Proc. Third Ann. Int'l Computing and Combinatorics Conf., (COCOON '97), pp. 232-241, 1997.
12. A. D'atri and M. Moscarini, "Distance-Hereditary Graphs, Steiner Trees, and Connected Domination," SIAM J. Computing, vol. 17, no. 3, pp. 521-538, 1988.
13. F.F. Dragan, "Dominating Cliques in Distance-Hereditary Graphs," Proc. Fourth Scandinavian Workshop Algorithm Theory (SWAT '94), pp. 370-381, 1994.
14. A. Esfahanian and O.R. Oellermann, "Distance-Hereditary Graphs and Multidestination Message-Routing in Multicomputers," J. Combinatorial Math. and Combinatorial Computing, vol. 13, pp. 213-222, 1993.
15. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs. New York: Academic Press, 1980.
16. P.L. Hammer and F. Maffray, "Complete Separable Graphs," Discrete Applied Math., vol. 27, no. 1, pp. 85-99, 1990.
17. X. He, "Efficient Parallel Algorithms for Solving Some Tree Problems," Proc. 24th Allerton Conf. Communication, Control, and Computing, pp. 777-786, 1986.
18. X. He, "Efficient Parallel Algorithms for Series-Parallel Graphs," J. Algorithms, vol. 12, pp. 409-430, 1991.
19. X. He and Y. Yesha, "Binary Tree Algebraic Computation and Parallel Algorithms for Simple Graphs," J. Algorithms, vol. 9, pp. 92-113, 1988.
20. E. Howorka, "A Characterization of Distance-Hereditary Graphs," Quarterly J. Math. (Oxford), vol. 28, no. 2, pp. 417-420, 1977.
21. S.-Y. Hsieh, C.W. Ho, T.-S. Hsu, M.T. Ko and G.H. Chen, "Efficient Parallel Algorithms on Distance-Hereditary Graphs," Parallel Processing Letters, vol. 9, no. 1, pp. 43-52, 1999.
22. S.-Y. Hsieh, "Parallel Decomposition of Distance-Hereditary Graphs," Proc. Fourth Int'l ACPC Conf. including Special Tracks on Parallel Numerics (ParNum'99) and Parallel Computing in Image Processing, Video Processing, and Multimedia, pp. 417-426, 1999.
23. S.-Y. Hsieh, C.W. Ho, T.-S. Hsu, M.T. Ko, and G.H. Chen, "A Faster Implementation of a Parallel Tree Contraction Scheme and Its Application on Distance-Hereditary Graphs," J. Algorithms, vol. 35, pp. 50-81, 2000.
24. S.-Y. Hsieh, C.W. HO, T.-S. Hsu, M.T. Ko, and G.H. Chen, "Characterization of Efficiently Solvable Problems on Distance-Hereditary Graphs," Proc. 8th Int'l Symp. Algorithms and Computation (ISAAC '98), pp. 257-266, 1998.
25. R.M. Karp and V. Ramachandran, "Parallel Algorithms for Shared Memory Machines," Handbook of Theoretical Computer Science, Amsterdam: North-Holland, pp. 869-941, 1990.
26. M. Livingston and Q.F. Stout, "Perfect Dominating Sets," Congressus Numerantium, vol. 79, pp. 187-203, 1990.
27. C.L. Lu and C.Y. Tang, "Efficient Domination on Bipartite Graphs," Manuscript, 1996.
28. H. Müller and F. Nicolai, "Polynomial Time Algorithms for Hamiltonian Problems on Bipartite Distance-Hereditary Graphs," Information Processing Letters, vol. 46, no. 5, pp. 225-230.
29. F. Nicolai, "Hamiltonian Problems on Distance-Hereditary Graphs," Technique Report SM-DU-264, Univ. Duisburg, Germany, 1994.
30. O.R. Oellermann, "Computing the Average Distance of a Distance-Hereditary Graph in Linear Time," Congressus Numerantium, vol. 103, pp. 219-223, 1994.
31. H.G. Yeh and G.J. Chang, "Weighted Connected Domination and Steiner Trees in Distance-Hereditary Graphs," Discrete Applied Math., vol. 87, pp. 245-253, 1998.
32. C.C. Yen, "Algorithmic Aspects of Perfect Domination," PhD thesis, Department of Computer Science, National Tsing Hua Univ., Taiwan, 1992.
33. C.C. Yen, R.C.T. Lee, "The Weighted Perfect Domination Problem and Its Variants," Discrete Applied Math., vol. 66, pp. 147-160, 1996.