[+] Approximation schemes in planar graphs: Branchwidth and Baker's technique. 

In this lecture we introduce two additional graph decompositions  carving decomposition and branch decomposition. We prove a theorem of Tamaki that roughly says that the branchwidth of a planar graph is at most twice its radius. We use the radius bound on the width of a decomposition of planar graphs to devise a PTAS for minimum vertex cover. This PTAS is an example of a general technique due to Baker, which can be applied to many other problems. 
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