Download presentation

Presentation is loading. Please wait.

Published byPayton Edrington Modified over 3 years ago

2
2

4
4 Theorem:Proof: What shall we do for an undirected graph?

5
5

6
6

7
7 p 0 (s)=1 p 1 (a)=0.5

8
8

9
9

10
10

11
11

12
12

13
Note that if the right answer is ‘NO’, we clearly answer ‘NO’. Hence, this random walk algorithm has one-sided error. Such algorithms are called “Monte-Carlo” algorithms. Complexi ty 13

14
14 st... The probability we head in the right direction is 1/d s But every time we get here, we get a second chance!

15
Since expectedly we return to each vertex within|E|/d i steps The walk expectedly heads in the right direction within 2|E| steps By linearity of the expectation, it is expected to reach t within d(s,t) 2|E| 2|V| |E| steps. 15 Complexity

16
1. Run the random walk from s for 2|V| |E| steps. 2. If node t is ever visited, answer “there is a path from s to t”. 3. Otherwise, reply “there is probably no path from s to t”. 16 Complexity

17
Theorem: The above algorithm - uses logarithmic space - always right for ‘NO’ instances. - errs with probability at most ½ for ‘YES’ instances. 17 Complexity To maintain the current position we only need log|V| space Markov: Pr(X>2E[X])<½ PAP 401-404

18
We explored the undirected connectivity problem. We saw a log-space randomized algorithm for this problem. We used an important technique called random walks. 18 Complexity

Similar presentations

OK

1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on social contract theory pdf Ppt on eddy current loss Ppt on pricing policy and strategy Ppt on guru granth sahib Ppt on levels of strategic management Ppt on total parenteral nutrition calculations Ppt on fibonacci sequence Ppt on waxes are lipids Conjunctions for kids ppt on batteries Jit ppt on manufacturing engineering