1+7-1-1=(5+7+7) |

(1)

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

| ^/

sattetshneesiponnffouet

f ^The ^analysis

for

^FIRF

is the same as before

# _F)

⁼

FEI

₎ ^-

FE

, ^whew approximated

with # ^an F- ^. iyiz _, ^. ^. _, is _, ^. ^. ^.

( if ^, >.< ⁱⁿ ^,tD

,

. .

f ^is, ZD^.

.

(2)

@ HFIKFEIFEH

=HE¥HE¥ ]

observations

xo

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^.

(3)

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 ^expensive_error _is ^, ^cost_additive

^Oftxti _? ⁾

^time

(4)

Fg

, >

=

Fsa

⁺

Esottjizt Fb

°Y?¥ews

_is

Tridents

Fi 16

⇒ to

[email protected]

(5)

old

^thus

^many^du

There ^ntnztnqt

^counters ^. ^. ^. ^< ²ⁿ

^dyadic

^intervals ^and

Fab

Old

When

FE 's )

^t=zs ^is ^execute , we also perform

Fay

^t= ^Zs

^for

êach înterval ^such ^that â

^tie

^}

( ^we _change

by

^w ^counters ^at ^most

)

0¥

^Given ^a _query

_Fxy

, the latter can be expressed ^as ^the ^sum of ^{

2GW

^dyadic întervals ⁽ îndeed ^, îf ^there ^were ⁵ consecutive

intern ^'s on the same level

, then ^we could replace ^two

of

^them by ân înterval ôf ^double ^site ôn ^the ûpper ^level

)

Fxy ⁼ Fas fab

(6)

We use count ^. ^min sketches on the counters Fab ^was

#

s

, thus

FI

,

,E¥b

⁼

1 cost is 0

(G)

^time

2 error is bounded

Fxye Fxyt 2e§w

^HFH ^with ^prob^. ^> ¹ ^-8

Let's see 2

(7)

Define

^Xsdp ^as ^the_garbage

for

^Fab _, ^that ^is

Fab ⁼

Fatty

^.

Let X ⁼

Expo

-

Observe

that ¥

,

Eytxxy

=

^Ekxi

^and ^that

⁾

⁼

_2{GI

^HFH

then

Pv[ Xxy

^> ^2e ^GNHFD _<

E[X×D

¥75 ±

The rest is identical

. o

Note _Using ^the îndividual êrrors ôn êacw

# ?

^{does not} ^work ^?

That ^is _, Pr # ^Yi ^>

EHFID

^does ^not imply^the ^above ^result