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, N ) space, but it can be segmented among level curves as in Appendix B.1 to use O N 1/2+o(N ) Note that in what follows objects are passed to functions as references. The code for some functions has been omitted

W. Computewheelmodulus,

U. Computeunitsmod,

, create three empty lists of pairs L1, L2 and L3

L. Constructprincipaldomain,

, create an empty min priority queue Q that only stores values

W. Insertvaluesfromdomain-(-q,

, Q.Insert(?

, create an empty queue S

S. Eliminateeven,

, Print all the primes dividing W ; EliminateSquaresAndPrint(S)

, Stony Brook, NY 11794-2424 USA. Email: {bender, rob, smccauley,shiksingh}@cs.stonybrook.edu. ? MS 1326

?. Po and . Box, Email: tmkroeg@sandia.gov. § LIP, ENS de Lyon, 46 allee d'Italie

, Intel Corporation, 2200 Mission College Blvd

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I. Os and . Point, log B N ) I/Os for in- serts/deletes Range queries returning k elements run in O(log B N + k/B) I/Os In contrast, the best possible highprobability bounds for inserting into the folklore B-skip list, which promotes elements with probability 1/B, is just ?(log N ) I/Os. This is no better than the bounds one gets from running an inmemory skip list in external memory

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