Download presentation

Presentation is loading. Please wait.

Published byEzequiel Danford Modified over 6 years ago

2
Every edge is in a red ellipse (the bags). The bags are connected in a tree. The bags an original vertex is part of are connected.

3
The root

5
Directed Weighted w3 w1 w2 w5 w9 w11 w8 w10 w7 w6 w4

6
Recursively build paths: O(n k ) Can there be algorithms with runtimes on the form f(k)n O(1) ? … and if so, how small can f(k) be?

7
Consider regular graphs of degree d: Either d>k: There must be k-path. Or d<=k: We can list all potential k-paths in nd k <=nk k time.

8
<k? B1 B2 B3 B4 B5 B6 Depth First Search

9
B1B2B3 B4 B5 B6

10
13 5 246 Prob[rainbow k-path] >= k!/k k ~ e -k

11
Dynamic programming over color subsets. Let D(X,v,k) be True iff there is a path of length k ending in vertex v whose vertices are colored as X.

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google