<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
are	O
a	O
kind	O
of	O
distributed	B-Architecture
data	B-General_Concept
structure	I-General_Concept
based	O
on	O
skip	O
lists	O
.	O
</s>
<s>
A	O
nearly	O
identical	O
data	B-General_Concept
structure	I-General_Concept
called	O
SkipNet	O
was	O
independently	O
invented	O
by	O
Nicholas	O
Harvey	O
,	O
Michael	O
Jones	O
,	O
Stefan	O
Saroiu	O
,	O
Marvin	O
Theimer	O
and	O
Alec	O
Wolman	O
,	O
also	O
in	O
2003	O
.	O
</s>
<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
have	O
the	O
full	O
functionality	O
of	O
a	O
balanced	B-Data_Structure
tree	I-Data_Structure
in	O
a	O
distributed	B-Architecture
system	I-Architecture
.	O
</s>
<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
are	O
mostly	O
used	O
in	O
searching	O
peer-to-peer	O
networks	O
.	O
</s>
<s>
As	O
they	O
provide	O
the	O
ability	O
to	O
query	O
by	O
key	O
ordering	O
,	O
they	O
improve	O
over	O
search	O
tools	O
based	O
on	O
the	O
hash	B-Algorithm
table	I-Algorithm
functionality	O
only	O
.	O
</s>
<s>
In	O
contrast	O
to	O
skip	O
lists	O
and	O
other	O
tree	B-Application
data	I-Application
structures	I-Application
,	O
they	O
are	O
very	O
resilient	O
and	O
can	O
tolerate	O
a	O
large	O
fraction	O
of	O
node	O
failures	O
.	O
</s>
<s>
In	O
addition	O
,	O
constructing	O
,	O
inserting	O
,	O
searching	O
,	O
and	O
repairing	O
a	O
skip	B-Data_Structure
graph	I-Data_Structure
that	O
was	O
disturbed	O
by	O
failing	O
nodes	O
can	O
be	O
done	O
by	O
straightforward	O
algorithms	O
.	O
</s>
<s>
A	O
skip	B-Data_Structure
graph	I-Data_Structure
is	O
a	O
distributed	B-Architecture
data	B-General_Concept
structure	I-General_Concept
based	O
on	O
skip	O
lists	O
designed	O
to	O
resemble	O
a	O
balanced	B-Data_Structure
search	I-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
They	O
are	O
one	O
of	O
several	O
methods	O
to	O
implement	O
a	O
distributed	B-Operating_System
hash	I-Operating_System
table	I-Operating_System
,	O
which	O
are	O
used	O
to	O
locate	O
resources	O
stored	O
in	O
different	O
locations	O
across	O
a	O
network	O
,	O
given	O
the	O
name	O
(	O
or	O
key	O
)	O
of	O
the	O
resource	O
.	O
</s>
<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
offer	O
several	O
benefits	O
over	O
other	O
distributed	B-Operating_System
hash	I-Operating_System
table	I-Operating_System
schemes	O
such	O
as	O
Chord	B-Application
(	O
peer-to-peer	O
)	O
and	O
Tapestry	O
(	O
DHT	O
)	O
,	O
including	O
addition	O
and	O
deletion	O
in	O
expected	O
logarithmic	O
time	O
,	O
logarithmic	O
space	O
per	O
resource	O
to	O
store	O
indexing	O
information	O
,	O
no	O
required	O
knowledge	O
of	O
the	O
number	O
of	O
nodes	O
in	O
a	O
set	O
and	O
support	O
for	O
complex	O
range	O
queries	O
.	O
</s>
<s>
A	O
major	O
distinction	O
from	O
Chord	B-Application
and	O
Tapestry	O
is	O
that	O
there	O
is	O
no	O
hashing	O
of	O
search	O
keys	O
of	O
resources	O
,	O
which	O
allows	O
related	O
resources	O
to	O
be	O
near	O
each	O
other	O
in	O
the	O
skip	B-Data_Structure
graph	I-Data_Structure
;	O
this	O
property	O
makes	O
searches	O
for	O
values	O
within	O
a	O
given	O
range	O
feasible	O
.	O
</s>
<s>
Another	O
strength	O
of	O
skip	B-Data_Structure
graphs	I-Data_Structure
is	O
the	O
resilience	O
to	O
node	O
failure	O
in	O
both	O
random	O
and	O
adversarial	B-Algorithm
failure	O
models	O
.	O
</s>
<s>
Level	O
0	O
consists	O
of	O
one	O
doubly	B-Data_Structure
linked	I-Data_Structure
list	I-Data_Structure
containing	O
all	O
of	O
the	O
nodes	O
in	O
the	O
set	O
.	O
</s>
<s>
Where	O
skip	B-Data_Structure
graphs	I-Data_Structure
differ	O
from	O
skip	O
lists	O
is	O
that	O
each	O
level	O
i≥1	O
,	O
will	O
contain	O
multiple	O
lists	O
;	O
membership	O
of	O
a	O
key	O
x	O
in	O
a	O
list	O
is	O
defined	O
by	O
the	O
membership	O
vector	O
.	O
</s>
<s>
The	O
membership	O
vector	O
is	O
defined	O
as	O
an	O
infinite	O
random	O
word	O
over	O
a	O
fixed	O
alphabet	O
,	O
each	O
list	O
in	O
the	O
skip	B-Data_Structure
graph	I-Data_Structure
is	O
identified	O
by	O
a	O
finite	O
word	O
w	O
from	O
the	O
same	O
alphabet	O
,	O
if	O
that	O
word	O
is	O
a	O
prefix	O
of	O
then	O
node	O
x	O
is	O
a	O
member	O
of	O
the	O
list	O
.	O
</s>
<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
support	O
the	O
basic	O
operations	O
of	O
search	O
,	O
insert	O
and	O
delete	O
.	O
</s>
<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
will	O
also	O
support	O
the	O
more	O
complex	O
range	O
search	O
operation	O
.	O
</s>
<s>
The	O
search	O
algorithm	O
for	O
skip	B-Data_Structure
graphs	I-Data_Structure
is	O
almost	O
identical	O
to	O
the	O
search	O
algorithm	O
for	O
skip	O
lists	O
but	O
it	O
is	O
modified	O
to	O
run	O
in	O
a	O
distributed	B-Architecture
system	I-Architecture
.	O
</s>
<s>
Analysis	O
performed	O
by	O
William	O
Pugh	O
shows	O
that	O
on	O
average	O
,	O
a	O
skip	O
list	O
and	O
by	O
extension	O
a	O
skip	B-Data_Structure
graph	I-Data_Structure
contains	O
levels	O
for	O
a	O
fixed	O
value	O
of	O
.	O
</s>
<s>
Insertion	O
is	O
done	O
in	O
two	O
phases	O
and	O
requires	O
that	O
a	O
new	O
node	O
knows	O
some	O
introducing	O
node	O
;	O
the	O
introducing	O
node	O
may	O
be	O
any	O
other	O
node	O
currently	O
in	O
the	O
skip	B-Data_Structure
graph	I-Data_Structure
.	O
</s>
<s>
Insertion	O
at	O
each	O
level	O
is	O
performed	O
using	O
standard	O
doubly	B-Data_Structure
linked	I-Data_Structure
list	I-Data_Structure
operations	O
;	O
the	O
left	O
neighbor	O
's	O
next	O
pointer	O
is	O
changed	O
to	O
point	O
to	O
the	O
new	O
node	O
and	O
the	O
right	O
neighbor	O
's	O
previous	O
pointer	O
is	O
changed	O
to	O
point	O
to	O
the	O
node	O
.	O
</s>
<s>
The	O
skip	B-Data_Structure
graph	I-Data_Structure
contains	O
an	O
average	O
of	O
O(log n )	O
levels	O
;	O
at	O
each	O
level	O
u	O
must	O
send	O
2	O
messages	O
to	O
complete	O
a	O
delete	O
operation	O
on	O
a	O
doubly	B-Data_Structure
linked	I-Data_Structure
list	I-Data_Structure
.	O
</s>
<s>
In	O
skip	B-Data_Structure
graphs	I-Data_Structure
,	O
fault	O
tolerance	O
describes	O
the	O
number	O
of	O
nodes	O
which	O
can	O
be	O
disconnected	O
from	O
the	O
skip	B-Data_Structure
graph	I-Data_Structure
by	O
failures	O
of	O
other	O
nodes	O
.	O
</s>
<s>
Two	O
failure	O
models	O
have	O
been	O
examined	O
;	O
random	O
failures	O
and	O
adversarial	B-Algorithm
failures	O
.	O
</s>
<s>
The	O
adversarial	B-Algorithm
model	I-Algorithm
assumes	O
node	O
failures	O
are	O
planned	O
such	O
that	O
the	O
worst	O
possible	O
failure	O
is	O
achieved	O
at	O
each	O
step	O
,	O
the	O
entire	O
skip	B-Data_Structure
graph	I-Data_Structure
structure	O
is	O
known	O
and	O
failures	O
are	O
chosen	O
to	O
maximize	O
node	O
disconnection	O
.	O
</s>
<s>
A	O
drawback	O
of	O
skip	B-Data_Structure
graphs	I-Data_Structure
is	O
that	O
there	O
is	O
no	O
repair	O
mechanism	O
;	O
currently	O
the	O
only	O
way	O
to	O
remove	O
and	O
to	O
repair	O
a	O
skip	B-Data_Structure
graph	I-Data_Structure
is	O
to	O
build	O
a	O
new	O
skip	B-Data_Structure
graph	I-Data_Structure
with	O
surviving	O
nodes	O
.	O
</s>
<s>
Skip	B-Data_Structure
graphs	I-Data_Structure
are	O
highly	O
resistant	O
to	O
random	O
failures	O
.	O
</s>
<s>
While	O
the	O
number	O
of	O
failed	O
nodes	O
is	O
less	O
than	O
the	O
skip	B-Data_Structure
graph	I-Data_Structure
can	O
continue	O
to	O
function	O
normally	O
.	O
</s>
<s>
Simulations	O
performed	O
by	O
James	O
Aspnes	O
show	O
that	O
a	O
skip	B-Data_Structure
graph	I-Data_Structure
with	O
131072	O
nodes	O
was	O
able	O
tolerate	O
up	O
to	O
60%	O
of	O
its	O
nodes	O
failing	O
before	O
surviving	O
nodes	O
were	O
isolated	O
.	O
</s>
<s>
While	O
other	O
distributed	B-Architecture
data	B-General_Concept
structures	I-General_Concept
may	O
be	O
able	O
to	O
achieve	O
higher	O
levels	O
of	O
resiliency	O
they	O
tend	O
to	O
be	O
much	O
more	O
complex	O
.	O
</s>
<s>
Adversarial	B-Algorithm
failure	O
is	O
difficult	O
to	O
simulate	O
in	O
a	O
large	O
network	O
as	O
it	O
becomes	O
difficult	O
to	O
find	O
worst	O
case	O
failure	O
patterns	O
.	O
</s>
<s>
If	O
skip	B-Data_Structure
graphs	I-Data_Structure
have	O
a	O
sufficiently	O
large	O
expansion	O
ratio	O
of	O
then	O
at	O
most	O
nodes	O
may	O
be	O
separated	O
,	O
even	O
if	O
up	O
to	O
f	O
failures	O
are	O
specifically	O
targeted	O
.	O
</s>
