[+] Branch decomposition and Tamaki's theorem |
We define carving and branch decompositions and show how to solve vertex cover using a dynamic program on the branch decomposition. Given a planar graph, we show how to find a carving decomposition whose width is related to the radius of the dual graph. We use this to prove Tamaki's theorem which shows (algorithmically) the existence of a branch decomposition whose width is roughly twice the minimum between the primal and dual radii. |
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Lecture notes, page 1/16 •
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