Abstract
The sequential complexity of various tree embedding problems arises in the recent work by Robertson and Seymour on graph minors; here we consider the parallel complexity of such problems. In particular, we present two CREW PRAM algorithms: an O(n 4.5)-processor O(log3 n) time randomized algorithm for determining whether there is a topological embedding of one tree in another and an O(n 4.5)-processor O(log3 n log log n) time randomized algorithm for determining whether or not a tree with a degree constraint is a minor of a general tree. These algorithms are two examples of a general technique that can be used for solving other problems on trees. One by-product of this technique is an NC reduction of tree problems to matching problems.
Research partially performed while the author was a NSERC postdoctoral fellow in the Department of Combinatorics and Optimization, University of Waterloo. Research supported by the Natural Sciences and Engineering Research Council of Canada, the Center for System Sciences and a President's Research Grant, Simon Fraser University.
Research supported by the Natural Sciences and Engineering Research Council of Canada.
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© 1992 Springer-Verlag Berlin Heidelberg
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Gupta, A., Nishimura, N. (1992). The parallel complexity of tree embedding problems (extended abstract). In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_170
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DOI: https://doi.org/10.1007/3-540-55210-3_170
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