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ICSI | ICSIhttp.icsi.berkeley.edu/ftp/pub/techreports/1993/tr-93-072...! "$#&%(' )+*, )+! #+* -.#&/0! 1 2324242524242324232424252424232424252424232424232425242423242 6 0 798:*5)+!

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Page 1: ICSI | ICSIhttp.icsi.berkeley.edu/ftp/pub/techreports/1993/tr-93-072...! "$#&%(' )+*, )+! #+* -.#&/0! 1 2324242524242324232424252424232424252424232424232425242423242 6 0 798:*5)+!

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O(log n) words

4n "buckets"

in e

ach

buck

et

1 2 4n−1 4n

A: x1 x2 x3 ... xn

v1 v2 v3 ... vn

virtual block ofmemory of size n

must store into a"hash−table" with4n buckets of sizeO(log n) each.

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Level (1) bufferwith four buckets

level (i) buffer with 4buckets

i

Level (2) buffer with4*4 buckets

Level N bufferwith 4t buckets

LOWER LEVEL BUFFERS

HIGHER LEVEL BUFFERS

buckets of size

O(log t) words each

Index s1for level (1)

Index s2for level (2)

Index sifor level (i)

Index sNfor level (N)

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Buffer A with n buckets.

Buffer B with 4n buckets

m words in

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m words in

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Jointly, buckets inboth A and B containat most n words

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1 2 3 4 5nm−1 5nm1

C: ...

Non−emtpy words and"dummy" words, with tagsfrom 1 through 4n.

("dummy" words ensure that ALLtags from 1 to 4n are represented)

Empty words with "0" tag

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1 2 3 4 5nm−1 5nm1

1 2 3 4 5nm−1 5nm1

Going from C to C’

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1 2 3 4 5nm−1 5nm1

Collect all data with the same "tag" intoa single bucket by performing oblivious sorting on each pair of adjacent buckets,going left to right

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perform "oblivious sort" ofbuckets, accumulating all 4nreal buckets in (5nm−4n) to 5mnpositions of C’

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