Abstract
We consider a special variant of tree-decompositions, called domino tree-decompositions, and the related notion of domino treewidth. In a domino tree-decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant C k,d such that a graph with treewidth at most k and maximum degree at most d has domino treewidth at most C k,d The domino treewidth of a tree can be computed in O(n 2 log n) time. There exist polynomial time algorithms that — for fixed k — decide whether a given graph G has domino treewidth at most k. If k is not fixed, this problem is NP-complete. The domino treewidth problem is hard for the complexity classes W[t] for all t ξ N, and hence the problem for fixed k is unlikely to be solvable in O(n c), where c is a constant, not depending on k.
This author was partially supported by the ESPRIT Basic Research Actions of the EC under contract 7141 (project ALCOM II).
This author was supported by the ESPRIT Basic Research Working Group COMPUGRAPH II.
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References
S. Arnborg, D. G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth., 8:277–284, 1987.
H. L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. In Proceedings of the 25th Annual Symposium on Theory of Computing, pages 226–234, New York, 1993. ACM Press.
H. L. Bodlaender. A tourist guide through treewidth. Acta Cybernetica, 11:1–23, 1993.
H. L. Bodlaender, R. G. Downey, M. R. Fellows, and H. T. Wareham. The parameterized complexity of sequence alignment and consensus (extended abstract). To appear in: proceedings Conference on Pattern Matching '94, 1993.
H. L. Bodlaender, M. R. Fellows, and M. Hallett. Beyond NP-completeness for problems of bounded width: Hardness for the W hierarchy. In Proceedings of the 26th Annual Symposium on Theory of Computing, pages 449–458, New York, 1994. ACM Press.
R. G. Downey and M. R. Fellows. Fixed-parameter tractability and completeness I: Basic results. Manuscript, 1991. To appear in SIAM J. Comput.
R. G. Downey and M. R. Fellows. Fixed-parameter tractability and completeness II: On completeness for W[1]. Manuscript, 1991. To appear in Theoretical Computer Science, Ser. A.
R. G. Downey and M. R. Fellows. Fixed-parameter tractability and completeness III: Some structural aspects of the W hierarchy. Technical Report DCS-191-IR, Department of Computer Science, University of Victoria, Victoria, B.C., Canada, 1992.
J. Engelfriet, L. M. Heyker, and G. Leih. Context-free graph languages of bounded degree are generated by Apex graph grammars. Acta Informatica, 31:341–378, 1994.
E. Horowitz and S. Sahni. Fundamentals of Computer Algorithms. Pitman, London, 1978.
T. Kloks, D. Kratsch, and H. Müller. Dominoes. This volume, pages 106–120, 1995.
B. Reed. Finding approximate separators and computing tree-width quickly. In Proceedings of the 24th Annual Symposium on Theory of Computing, pages 221–228, New York, 1992. ACM Press.
D. Seese. Tree-partite graphs and the complexity of algorithms. In L. Budach, editor, Proc. 1985 Int. Conf. on Fundamentals of Computation Theory, Lecture Notes in Computer Science 199, pages 412–421, Berlin, 1985. Springer Verlag.
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Bodlaender, H.L., Engelfriet, J. (1995). Domino treewidth. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_33
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DOI: https://doi.org/10.1007/3-540-59071-4_33
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