SLIDE 1
Space efficient
quantile selection
Input
stream
9 an C U
Where U has order C
000
11
e.g
numerical data
names
w
alphabetic order
grades
allowed multiple
passes
Goal
return
the median
w
minimum
a
I
pass
Input
exikhd.dk fT n
11 numerical data e.g alphabetic order names w grades allowed - - PDF document
11 numerical data e.g alphabetic order names w grades allowed - - PDF document
Space efficient quantile selection Where U has order C an C U stream Input 9 000 11 numerical data e.g alphabetic order names w grades allowed multiple passes median return the Goal minimum w 6 space passes a quantile queries
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i i kh
SLIDE 4
Passe
Spacey
1
Och
sort
and select
Ollogn
OCI
quickselect
random pivot
p
rib
Munro Paterson 1981
2
Vis
quantile
summaries
SLIDE 5
Approximations
given
rank
KEEN and
param
E
return
element
w
rank
k
En
f
K
Sampling
for median
18
elements sample
f return medias
- f sample
for
rank k dn
sample
l
return
rank
de
- ut
- f
the
sample
Deterministic
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Key
invariant
any
two
consecutive
intervals have width
E
2En
E APX
quantile summary
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Q
ai
get 94
9mi
w
intervals
3
To show Q
is
E APX
need
to
show
2Eb width
property
Take
two consecutive
intervals
in Q's
y E
g
Two
cases
elements
from
diff
sets
elements from
same
sets
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Recap
we
can
combine
E APX quantile summaries
to get
E APX quantile summary of
wholething
sparsify
E APX quantile summary
to
tat
APX
quantile summary
w Kpoints
Remains
to address
how
to
make
- ne
at
all
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Space
D
D
D D
D
D
D
D
D D D
D D D D
- nly keep
root summaries
SLIDE 23
theorem
1
pass
OClog4n
E
space deterministic
E
APX
quantile
- ver
stream
idea mergability
t dyadic intervals trick
slightly better
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Theoremett
1
pass
0ClogicEh 1E
space deterministic
E
APX
quantile
- ver
stream
Even better
Khanna
Greenwald 2001T
loafers
space
more sophisticated quantile
summary
merging
interval
trick
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