Abstract
We study several P-complete graph problems and show that they are in NC if the input graphs are restricted to be tree-structured. These graphs are also known as partial k-trees, decomposable graphs or graphs of bounded tree width, and include outerplanar graphs, series-parallel graphs and Halin graphs. The particular problems investigated herein include the lexicographically first (l.f.) depth-first search tree and the l.f. maximal independent set. It is also shown that if a tree of faces of an outerplanar graph is given, then its dfs tree can be found in O(log2n) time using O(n/log2n) processors.
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© 1989 Springer-Verlag Berlin Heidelberg
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Chlebus, B., Diks, K., Rytter, W., Szymacha, T. (1989). Parallel complexity of lexicographically first problems for tree-structured graphs. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_66
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DOI: https://doi.org/10.1007/3-540-51486-4_66
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