Abstract
The minimum all-ones problem is applied in linear cellular automata. It is NP-complete for general graphs. In this paper, we consider the problem for graphs with small treewidth≤4. We give an O(|V|) algorithm.
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Bondy, J.A., Murty, U.S.R.: Graph theory with application. Macmillan, London (1976)
Barua, R., Ramakrishnan, S.: σ-game, σ  + -game and two dimensional additive cellular automata. Theoret. Comput. Sci. 154, 349–366 (1996)
Dodis, Y., Winkler, P.: Universal configurations in light-flipping games. In: Proceedings of 12-th Annuaql ACM/SIAM Symposium on Discrete Algorithms(SODA), pp. 926–927. ACM Press, New York (2001)
Galvin, F.: Solution to problem 88-8. Math. Intelligencer 11, 31–32 (1989)
Sutner, K.: Problem 88-8. Math. Intelligencer 10 (1988)
Sutner, K.: Linear Cellular automata and the Garden-of-Eden. Math. Intelligencer 11, 49–53 (1989)
Sutner, K.: The σ game and cellular automata. Amer. Math. Monthly 97, 24–34 (1990)
Sutner, K.: σ-automata and Chebyshev-polynominals. Theoret. Comput. Sci. 230, 49–73 (2000)
Daniel, P.: Sanders: On linear recognition of tree-width at most four. SIAM J. Discrete Math. 9, 101–117 (1995)
Chen, Y.C., Li, X., Wang, C., Zhang, X.: The minimum all-ones problem for trees. SIAM J. Comput. 33, 379–392 (2003)
de Fluiter, B.: Algorithms for Graph of Small Treewidth. France (1997)
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Lu, Y., Li, Y. (2007). The Minimum All-Ones Problem for Graphs with Small Treewidth. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_35
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DOI: https://doi.org/10.1007/978-3-540-73556-4_35
Publisher Name: Springer, Berlin, Heidelberg
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