The Minimum All-Ones Problem for Trees

Authors:
William Y. C. Chen;Xueliang Li;Chao Wang;Xiaoyan Zhang
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Computing
Year:
2004

Citing 0
Cited 5

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Does the lit-only restriction make any difference for the σ-game and σ+-game?

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The minimum all-ones problem for graphs with small treewidth

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Abstract

The minimum all-ones problem was shown to be NP-complete for general graphs. Therefore, it becomes an interesting problem to identify special classes of graphs for which one can find polynomial time algorithms. In this paper we consider this problem for trees. First, for any solution to the all-ones problem for a tree, we give a characterization of the elements in the solution by introducing the concept of the quasi all-ones problem. Then we give the enumeration for the number of solutions in a tree. By using the minimum odd (even) sum problem as subprocess, we obtain a linear time algorithm for the minimum all-ones problem for trees. We also get a linear time algorithm for finding solutions to the all-ones problem in a unicyclic graph.