Abstract
We introduce here a generic problem component and algorithms for it on various parallel models, that captures the most common, difficult "kernel" of many types of problems, e.g. geometric dominance. This kernel involves general prefix computations (GPCs) that can, with insight, be done quickly in parallel and by iterative techniques. GPCs' lower bound complexity of Ω (n log n) time is established, and we give optimal solutions on the sequential model in0(n log n) time, on the CREW PRAM model in 0(log n) time with n processors, on the BSR (broadcasting with selective reduction) model in constant time using n processors, and on mesh-connected computers in 0(✓n) time with (✓n) processors. A solution in 0(log 2 n) time on the hypercube model is given which is the best possible given known sorting limitations. We show that general prefix techniques can be applied to a wide variety of geometric (point set and tree) problems, including triangulation of point sets, two-set dominance counting, ECDF searching, finding two- and three-dimensional maximal points, and the (classical) reconstruction of trees from their traversals. In sum, GPC techniques have many important consequences.
work partially supported by NSF IRI 8709726.
work partially supported by NSERC.
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© 1989 Springer-Verlag Berlin Heidelberg
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Springsteel, F., Stojmenović, I. (1989). Parallel general prefix computations with geometric, algebraic and other applications. In: Csirik, J., Demetrovics, J., Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1989. Lecture Notes in Computer Science, vol 380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51498-8_41
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DOI: https://doi.org/10.1007/3-540-51498-8_41
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