Download presentation
Presentation is loading. Please wait.
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
![Prob[rainbow k-path] >= k!/k k ~ e -k](http://images.slideplayer.com./11/3252114/slides/slide_10.jpg "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
![1 Representing Graphs. 2 Adjacency Matrix Suppose we have a graph G with n nodes. The adjacency matrix is the n x n matrix A=[a ij ] with: a ij = 1 if.](/15/4821664/big_thumb.jpg "1 Representing Graphs. 2 Adjacency Matrix Suppose we have a graph G with n nodes. The adjacency matrix is the n x n matrix A=[a ij ] with: a ij = 1 if.>")
