Tree inclusion problems.(English)Zbl 1149.68040

Summary: Given two trees (a target $$T$$ and a pattern $$P$$) and a natural number $$w$$, window embedded subtree problems consist in deciding whether $$P$$ occurs as an embedded subtree of $$T$$ and/or finding the number of size (at most) $$w$$ windows of $$T$$ which contain pattern $$P$$ as an embedded subtree. $$P$$ is an embedded subtree of $$T$$ if $$P$$ can be obtained by deleting some nodes from $$T$$ (if a node $$v$$ is deleted, all edges adjacent to $$v$$ are also deleted, and outgoing edges are replaced by edges going from the parent of $$v$$ (if it exists) to the children of $$v$$). Deciding whether $$P$$ is an embedded subtree of $$T$$ is known to be NP-complete. Our algorithms run in time $$O(|T|2^{2^{|P|}} )$$ where $$|T|$$ (resp. $$|P|$$) is the size of $$T$$ (resp. $$P$$).

MSC:

 68Q25 Analysis of algorithms and problem complexity 68W05 Nonnumerical algorithms
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References:

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