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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.

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Presentation on theme: "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."— Presentation transcript:

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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

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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 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/11/3252114/slides/slide_8.jpg", "name": "

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.


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