Abstract
We show that any parallel algorithm in the fixed degree algebraic decision tree model that answers membership queries in W ⊑ R n using p processors, requires Ω(¦W¦/n log(p/n)) rounds where ¦W¦ is the number of connected components of W. We further prove a similar result for the average case complexity. We give applications of this result to various fundamental problems in computational geometry like convex-hull construction and trapezoidal decomposition and also present algorithms with matching upper bounds.
Part of the work was done when the author was visiting Max-Plank Institute for Informatik, Germany
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© 1994 Springer-Verlag Berlin Heidelberg
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Sen, S. (1994). Lower bounds for parallel algebraic decision trees, complexity of convex hulls and related problems. In: Thiagarajan, P.S. (eds) Foundation of Software Technology and Theoretical Computer Science. FSTTCS 1994. Lecture Notes in Computer Science, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58715-2_125
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DOI: https://doi.org/10.1007/3-540-58715-2_125
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