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Graph Inference from a Walk for Trees of Bounded Degree 3 is NP-Complete

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概要 The graph inference from a walk for a class $C$ of undirected edge-colored graphs is, given a string $x$ of colors, finding the smallest graph $G$ in $C$ that allows a traverse of all edges in $G$ who...se sequence of edge-colors is $x$, called a walk for $x$. We prove that the graph inference from a walk for trees of bounded degree $k$ is NP-complete for any $k gep 3$, while the problem for trees without any degree bound constraint is known to be solvable in $O(n)$ time, where $n$ is the length of the string. Furthermore, the problem for a special class of trees of bounded degree 3, called (1,1)-caterpillars, is shown NP- complete. This contrast with the case that the problem for linear chains is known to be solvable in $O(n log n)$ time since a (1,1)-caterpillar is obtained by attaching at most one edge to each node of a linear chain. We also show the MAXSNP-hardness of these problems.続きを見る

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登録日 2009.04.22
更新日 2017.01.20