6.896 Sublinear Time Algorithms
September 30, 2004
Lecture 6
Lecturer: Ronitt Rubinfeld
Scribe: Swastik Kopparty
1
Continuing the Proof of Correctness of the Bipartiteness Tester
We assume that the graph is
far from bipartite and need to show that the algorithm fails with proba
bility at least 2
/
3.
Recall that we partitioned the sample into 2 parts,
U
and
S
.
• 
U

=
m
1
= Θ(log
(
1
)
/
)
• 
S

=
m
2
=
Cm
1
/
U
induced a partition of all the vertices it covered into
C
1
,
C
2
. Also recall that
U
is
good
if less than
n/
4 inﬂuential nodes are not adjacent to some vertex in
U
.
Last time we showed that Pr
U
[
U
good
]
≥
5
/
6.
The other main result we carried over is that whenever
U
is good, then for
any
partition of the whole
graph, there are at least
n
2
/
3 violating edges between
C
1
, C
2
(that is an edge between 2 vertices in the
same
C
i
). Now we will finish off the proof by showing that this implies that if
U
is good, then with high
probability
U
∪
S
will not be bipartite.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '04
 RonittRubinfeld
 Algorithms, Graph Theory, The Edge, Bipartiteness Tester

Click to edit the document details