Abstract
We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function f G of a graph G on n vertices. Our results are as follows:
-) For graphs of bounded tree-width there is an OBDD of size O(logn) for f G that uses encodings of size O(logn) for the vertices;
-) For graphs of bounded clique-width there is an OBDD of size O(n) for f G that uses encodings of size O(n) for the vertices;
-) For graphs of bounded clique-width such that there is a reduced term for G (to be defined below) that is balanced with depth O(logn) there is an OBDD of size O(n) for f G that uses encodings of size O(logn) for the vertices;
-) For cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for f G that uses encodings of size O(logn) for the vertices. This last result improves a recent result by Nunkesser and Woelfel [14].
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Arnborg, S., Lagergren, J., Seese, D.: Easy problems for tree decomposable graphs. Journal of Algorithms 12, 308–340 (1991)
Bodlaender, H.L.: NC-algorithms for graphs with small tree-width. In: van Leeuwen, J. (ed.) WG 1988. LNCS, vol. 344, pp. 1–10. Springer, Heidelberg (1989)
Breitbart, Y., Hunt, H., Rosenkrantz, D.: On the size of binary decision diagrams representing Boolean functions. Theoretical Computer Science 145(1), 45–69 (1995)
Corneil, D.G., Lerchs, H., Stewart Burlingham, L.: Complement reducible graphs. Discrete Applied Mathematics 3, 163–174 (1981)
Courcelle, B.: Graph grammars, monadic second-order logic and the theory of graph minors. Contemporary Mathematics 147, 565–590 (1993)
Courcelle, B., Makowsky, J.A., Rotics, U.: Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width. Theory of Computing Systems 33(2), 125–150 (2000)
Courcelle, B., Mosbah, M.: Monadic second-order evaluations on tree decomposable graphs. Theoretical Computer Science 109, 49–82 (1993)
Courcelle, B., Olariu, S.: Upper bounds to the clique-width of graphs. Discrete Applied Mathematics 101, 77–114 (2000)
Feigenbaum, J., Kannan, S., Vardi, M.Y., Viswanathan, M.: Complexity of Problems on Graphs Represented as OBDDs. Chicago Journal of Theoretical Computer Science 1999(5/6), 1–25 (1999)
Keeler, K., Westbrook, J.: Short encodings of planar graphs and maps. Discrete Applied Mathematics 58, 239–252 (1995)
Lozin, V., Rautenbach, D.: The Relative Clique-Width of a graph, Rutcor Research Report RRR 16-2004 (2004)
Miller, G., Reif, J.: Parallel tree contraction and its application. In: Proc. 26th Foundations of Computer Science FOCS 1985, pp. 478–489. IEEE, Los Alamitos (1985)
Naor, M.: Succinct representation of general unlabeled graphs. Discrete Applied Mathematics 28, 303–307 (1990)
Nunkesser, R., Woelfel, P.: Representation of Graphs by OBDDs. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 1132–1142. Springer, Heidelberg (2005)
Sawitzki, D.: Implicit Flow Maximization by Iterative Squaring. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2004. LNCS, vol. 2932, pp. 301–313. Springer, Heidelberg (2004)
Sawitzki, D.: A symbolic approach to the all-pairs shortest-paths problem. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 154–167. Springer, Heidelberg (2004)
Wegener, I.: Branching Programs and Binary Decision Diagrams: Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2000)
Woelfel, P.: Symbolic topological sorting with OBDDs. Journal of Discrete Algorithms (to appear)
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Meer, K., Rautenbach, D. (2006). On the OBDD Size for Graphs of Bounded Tree- and Clique-Width. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_7
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DOI: https://doi.org/10.1007/11847250_7
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