Abstract
In the literature, there are quite a few sequential and parallel algorithms to solve problems in a distance-hereditary graph G utilizing techniques discovered from the properties of the problems. Based on structural properties of G, we first sketch characteristics of problems which can be systematic solved on G and then define a general problem-solving paradigm. Given a decomposition tree representation of G, we propose a unified approach to construct sequential dynamic programming algorithms for several fundamental graph-theoretical problems that fit into our paradigm. We also show that our sequential solutions can be efficiently parallelized using the tree contraction technique.
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References
K. Abrahamson, N. Dadoun, D. G. Kirkpatrick, and T. Przytycka, A simple parallel tree contraction algorithm. Journal of Algorithms., 10, pp. 287–302, 1989.
H. J. Bandelt and H. M. Mulder. Distance-hereditary graphs. Journal of Combinatorial Theory Series B, 41(1):182–208, Augest 1989.
A. Brandstädt and F. F. Dragan, A linear time algorithm for connected γ-domination and Steiner tree on distance-hereditary graphs, Networks, 31:177–182, 1998.
M. S. Chang, S. Y. Hsieh, and G. H. Chen. Dynamic Programming on Distance-Hereditary Graphs. Proceedings of 7th International Symposium on Algorithms and Computation, ISAAC97, to appear.
E. Dahlhaus, ”Optimal (parallel) algorithms for the all-to-all vertices distance problem for certain graph classes,” Lecture notes in computer science 726, pp. 60–69.
E. Dahlhaus. Efficient parallel recognition algorithms of cographs and distancehereditary graphs. Discrete applied mathematics, 57(1):29–44, February 1995.
A. D’atri and M. Moscarini. Distance-hereditary graphs, steiner trees, and connected domination. SIAM Journal on Computing, 17(3):521–538, June, 1988.
F. F. Dragan, Dominating cliques in distance-hereditary graphs, Algorithm Theory-SWAT’94”4th Scandinavian Workshop on Algorithm Theory, LNCS 824, Springer, Berlin, pp. 370–381, 1994.
M. C. Golumbic. Algorithmic graph theory and perfect graphs, Academic press, New York, 1980.
P. L. Hammer and F. Maffray. Complete separable graphs. Discrete applied mathematics, 27(1):85–99, May 1990.
E. Howorka. A characterization of distance-hereditary graphs. Quarterly Journal of Mathematics (Oxford), 28(2):417–420. 1977.
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, to appear. A preliminary version of this paper is in Proceedings of the International Conference on Parallel Processing, pp. 20–23, 1997.
S.-y. Hsieh, C. W. Ho, T.-s. Hsu, M. T. Ko, and G. H. Chen. A new simple tree contraction scheme and its application on distance-hereditary graphs. Proceedings of Irregular’98, Springer-Verlag, to appear.
S.-y. Hsieh, Parallel decomposition of Distance-Hereditary Graphs with its application. Manuscript, 1998.
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Hsieh, SY., Ho, CW., Hsu, TS., Ko, MT., Chen, GH. (1998). Characterization of Efficiently Solvable Problems on Distance-Hereditary Graphs. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_28
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DOI: https://doi.org/10.1007/3-540-49381-6_28
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