FEPEO
: .ALLOWING
NEGATIVE counters' DEA FE
)=5
- 3-2+7 -1+7-1-1=(5+7+7)
-
(
3+2+1+1 + I )FED
-FI ]
Keep 2 count . min
| /
sattetshneesiponnffouetf The analysis
for
FIRFis the same as before
# F)
=FEI
) -FE
, whew approximatedwith # an F- . iyiz , . . , is , . . .
( if , >.< in ,tD
,
. .
f is, ZD.
.
@ HFIKFEIFEH
=HE¥HE¥ ]
observationsxo
Hot
=l¥gittlxIl= ¥
thief the
. "Prtkoil
>EHFIDC E[kiD ¥ EIXII
+Etxs :]
⇒
IFH EHFH
Markey
=
ftp.t/ineeueib@E#=te
we cdw bound the cnov in this way
the rest of the
analysis
is uhchguped.Interval
queues
< I
, ,t ,> < iz, t, > . . . . .
.li#
. . . .FF ) FE ) .
tFy
) .FE
.'s
P
+ Zs
simple query
:FE
. ]
Interval query : F[x]tFE⇒t . .
.+FE¥¥¥F×
,
=
FIFE
]Wrong way :
FI
, =JEFF
)#
12 expensiveerror is , costadditiveOftxti ? )
timeFg
, >=
Fsa
+Esottjizt Fb
°Y?¥ews
isTridents
Fi 16
⇒ to
yFkt@tGFgooEEEEEotFFI7FE7FEtED5c78Tcok12DklJknn.g
old
thus
manyduThere ntnztnqt
counters . . . < 2ndyadic
intervals andFab
Old
When
FE 's )
t=zs is execute , we also performFay
t= Zsfor
each interval such that atie
}( we change
by
w counters at most)
0¥
Given a queryFxy
, the latter can be expressed as the sum of {
2GW
dyadic intervals ( indeed , if there were 5 consecutiveintern 's on the same level
, then we could replace two
of
them by an interval of double site on the upper level)
Fxy = Fas fab
We use count . min sketches on the counters Fab was
#
s, thus
FI
,
,E¥b
=1 cost is 0
(G)
time2 error is bounded
Fxye Fxyt 2e§w
HFH with prob. > 1 -8Let's see 2
Define
Xsdp as thegarbagefor
Fab , that isFab =
Fatty
.Let X =
Expo
-
Observe
that ¥
,Eytxxy
=Ekxi
and that)
=2{GI
HFHthen
Pv[ Xxy
> 2e GNHFD <E[X×D
¥75 ±
The rest is identical
. o
Note Using the individual errors on eacw
# ?
does not work ?That is , Pr # Yi >