{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# l6 - 6.896 Sublinear Time Algorithms Lecture 6 Lecturer...

This preview shows pages 1–2. Sign up to view the full content.

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.

{[ snackBarMessage ]}

### Page1 / 2

l6 - 6.896 Sublinear Time Algorithms Lecture 6 Lecturer...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online