Finding large planar subgraphs and large subgraphs of a given genus
We consider the MAXIMUM PLANAR SUBGRAPH problem — given a graph G, find a largest planar subgraph of G. This problem has applications in circuit layout, facility layout, and graph drawing. We improve to 4/9 the best known approximation ratio for the MAXIMUM PLANAR SUBGRAPH problem. We also consider a generalization of the previous problem, the MAXIMUM GENUS D SUBGRAPH problem — given a connected graph G, find a maximum subgraph of G of genus at most D. For the latter problem, we present a simple algorithm whose approximation ratio is 1/4.
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