Comparison of Search Engines Non-Neutral and Neutral …
[Pages:4]Comparison of Search Engines Non-Neutral and Neutral Behaviors
Pierre Coucheney
Patrick Maill?
Inria Rennes Bretagne
T?l?com Bretagne
Atlantique
2, rue de la Ch?taigneraie
Campus Universitaire de
5576 Cesson S?vign? Cedex,
Beaulieu
France
35042 Rennes Cedex, France patrick.maille@telecom-
Pierre.Coucheney@inria.fr
bretagne.eu
Bruno Tuffin
Inria Rennes Bretagne Atlantique
Campus Universitaire de Beaulieu
35042 Rennes Cedex, France
Bruno.Tuffin@inria.fr
ABSTRACT
tr trt s rt ttrt t ttt t sr trt s s st s ss s tr sr rt s r t tt r ss srs rs ts r t t stts tr sr r r t rsts r t t rt sr rt r t st st r t s t sr s s tt t s t ss t r s t sr t t t s r r s t rtr trst stt s r sr t r r t tt st rs
Categories and Subject Descriptors
tr sts rt tr
t trstr rts
General Terms
s trt r s
1. INTRODUCTION
tr trt s r t t t
st rs t t s t r t ts s t rs t trt r t tts s tr s t r s tt trt sr rrs Ps tt r tt rrs Ps tr tr tr tr trs r rsr s t r tt Ps r rrsts rtt rs rt t tt trrt s tt Ps trt t s s ts t ts Ps t t tr ss r t r tr qt sr s t t trt r stt tt srs r tt t r tt tt ts s t rtt t st s r t rtsts r Ps srs ssts tr rss tt t t r s s t s t s r
Copyright is held by author/owner(s).
ss t s tt st t st rt rrs
r t t rt sss t trt Ps tt s trs sr s r str rtt t t s s r s ts ts s t t rst tt sr s r t trt s st ss srs s t r rr t r t st rt rt tt s sr st t Ps r srs t rt tt t t st s s sr rts s rtt sss t r t t trs t r r t r st ts sss s t t t r t tt rts r s rs r t ts t r r ssr s tt s t t t r t t rt t t t rsts t sr t t t sss sr s r s rtr s t r t r s
r s r s s sr
s r r t tr rrtss r t t t rs ts s tr r s r s t tr sr s r rs s tt r rt s tr sst r sr t r s tt tt t s s r s t t s rt
rr t s t r t tt
s s r t tst rt t st s t st s tt r tt r Ps t r r r r r tt s t ss r tt r r r t
ts r t s t rst tr r t r t t tr s s t r t rst r tt rt trs ss tr r rs t r t t sr s ss tt t r t t r srs s srs ss st s r ss sss
r
st
ttr
ts
rststr
tr t ts rt s t sr rsts t r s
trr sr t t s ssts r t rs t ts tr tr r r t stts tr t t sr s s s tt t ss t t tt rrs sr s r rt trst tt s t ss t r rqsts r r tr r tt s tr s strt r rs s rrs rrs t rs t t r s rst s rr t t ss ss tt t rrs r sts t t rrt stt trs t t t
2. MODEL DESCRIPTION
2.1 Users
sr rt rqsts (r) r t t tt s r t r r s s t t tr s ss t rs t
2.2 Content providers
sr t sr st m Ps t rqsts
s s r tt r rt t r
trst t r r P i s Ri ts r r P i s Gi
2.3 Search engine
sr s ss t s ss Ps
t t sts t s
st r s s rrt t m
Ps
t t t t r s tr t tr
rt ss rs t r t j t r j t 1 > 2 > ? ? ? > m.
sr s r (r) s t rr rt rqsts r tt s r r r m tt
rrs trst t t t rtrsts sr
r t r s
m
r=
(i) Ri
i=1
r (i) s t r P i
t tr s t r s s r
t Ri t tr s t s s t
r t rs t t sr
2.4 Utility functions
P i t tr s P t
t t tr s s tr ss t r r r t t r s t tr rt ss r ts t rtst t r t t r
UiP = (r)(i)Gi
t (i) t r P i
r t tr s t tr r r s
sr s h((r)) r h s ss r
r rs t r sts t r s rtst sts r s s t t
t tr s t tr s t ts
r s m < m r r t ts s t r ss t {1, . . . , m}
t t s Gi s t
t t r
m i=1
(r)(i)Gi.
s ss r rs t
ts ssr s t r
r ts rrt t P r i (r)(i)Gi.
t srs rr sr t tt t rt
(r) rrt s (r) = (r) t = ()
t rr rt rrs t t rqst rt
r r (r) t rt tt rr rqst ts r r rqrs r
r ss t t r s ststt
rqsts t rrt r tt r s
s t st rs rt t rr
ss t rqsts s r r r
t -1(/) s t st sst t strt t tt r t r srs rrs t
tt sr stst s
r
= y(y)dy.
0
3. NUMERICAL COMPARISON
s strt sr m = 3 rt s t (G1, R1) = (3, 2) (G2, R2) = (2, 3) (G3, R3) = (1, 1) t s i = 1/2i
(r) = min(r, 4).
rrs st s
(y) = 1/(4y)1{y(0,4]}
r r [0, 4] = r3/2/6 ss
r r r ssr s r t sr
h() =
tr r rst P t P
P t
3
r = (i)Ri = 17/8,
i=1
t rqst rt s = 17/8 1.4577
0.5163 r t
1.451777/8 U3PP0s.1r822s r
Ur1P
ssr
1.0933
U2Ps
s
sr t ss t ss t
tr
s t tt rt t t
sr t ts rrt t r
P s t
ts r s
U
=
3
h((r)) + (r) (i)Gi
i=1
3
3
=
(i)Ri + (i)Gi .
i=1
i=1
rt s ss rs t
t t r r P s t st s t st
t s t s t st rt t s
st rt s s s t t ssts P
s rst s tt U = U1 = 15/8( + 17/8)
r P s rst t tr r t s tt
U = tr
U2 = r
17/8( + 15/8).
U1
rr > U2 tt s
< (17 15/17/8-15/8)/(1- 15/17)
1.996. tr rs t r
r t rqst s t r t
rst t t rt r t r Ps t
s trst t tr r t
rtr r t trs tt ss
rt t s = 1 r rst
r r t Ps s rs
trs r t t tr
s = 0
5
s Ps tr
tr
4
s Ps tr
tr
3
s
2
1
0
0
0.2
0.4
0 50098 .
0.6
0.8
1
r s t ss t
t ts t r = 1 r s trst stt s Ps rs t t trs t r s r r t rt r s rst t s t tr tr ss r < 0.50098 s t r s t s t t s Ps t s r s s s t t Ps s t trs tt s t srs Ps s r trt
P s t
rs r ssr s t s r t tt s tt ts tt r s
U = h((r)) + (r)(1)G1
3
= ( + 3(1))
(i) Ri .
i=1
tr s s t U = 17/8( + 3/4).
Ut
s rst P r = 15/8( +3/2). r r
s r t t
r t trs s tt tr
r rrr < 3/2( 15/17 -
1/2)/(1 - 15/17) 10.8633. ts t r r ssr s s t r t r t P r trs t Ps s rs r s s r = 10.8633 t sst s tr
s tr Ps tr
20
tr
s tr Ps tr
tr
15
10
s
0.55
5
tr
tr
0
0
2
4
6
8
1010.863312
14
0.5
r s t s P
s
0.45
0
0.2
0.4
0 50098 .
0.6
0.8
1
r t ss t
t r tt t s s tr t Ps s t t t r t s t t
4. THE CASE OF A GENERAL SET OF KEY-
WORDS
t s r r trst t sr (r) s t tt rt rqsts t st r s r t r s rs r r tt s r tt st ss rqsts ss tt t sr s st rqst rrs tt t st Ps t s s tt t m Ps r t t s s r t r m t t ts r s st t r s P s r strt F t r t Ps t
0.55 0.5
tr tr
s
0.45
0.4 0
2
4
6
8
1010.863312
14
r t s P
s P s r strt G t t
Ps
trr st s t r strt
Ps trs r t
t Ps r r r s (r) s t
r r t t tr s r t
st rqsts s ststt t rt rqsts sr
stst s r r r
t tr s t r r r r
r rr sttsts s t r s s
r
m
r = j
j=1
y
(m
-
m! j-
1)!
j
!
F
(y)m-j-1(1
-
F
(y
))j
f
(y)dy.
r
r
P
s
E[U P]
=
(r)E[J G],
r J s t r r t P r {1, . . . , m}
s t r t s r
P r t s t t tr
s E[U ] = (r)E[J ]E[G].
t tr s t r s r
t t r tr t rt (r) t s
t t s trt s r t
tt rrt Ps rs t t s t tr t t r tts r ss rt ((R1, G1), . . . , (Rm, Gm)) t t t s
t s t tts s t s tt
m
= rrt h((r)) + (r)E
(j ) Gj
j=1
t r t r r s t s rtts
r s s s rr
t t t tt t rr sst t
trst s t t tr (r)
ss sst
t s trt s r t
P t s t t t t rtts
m
= rrt h((r)) + (r)E (j)Gj .
j=1
Acknowledgement
trs t t srt t r tr tr t s t rsr rt rs rt rsr t
5. REFERENCES
t t tr
trt t ss Pr tr s r
rr r
ss P ? t trt t t tt Ps
Prs t rt trt r t sts r r
P P ? tr trt t P trts r r st rt rt rr r
rrt t trt t s t
t t r tr t r rr ttsts s t
r trt Pt ts t t tr trt t t Pr t tt Prrt rtrs srs rrt
ttrsssrsrs strt
r t trt r t tr r trt rs t rr
st t
r ts Prs t rs ts
P ? rs ts r rsr ssr sr
ts tr r sr r
r
s t tt rrt r r t
q rts sr
P r r trss tr stt t s rts t t trt t rt rst s s rts r Prs rs
tr trt sr trt t r t t
rss rts tr s
r Pst ts trt r str rt
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