Parameterized complexity: exponential speed-up for planar graph problems

A parameterized problem is fixed parameter tractable if it admits a solving algorithm whose running time on input instance (I, k) is f(k)ċ|I|α, where f is an arbitrary function depending only on k. Typically, f is some exponential function, e.g., f(k) = ck for constant c. We describe general techniques to obtain growth of the form f(k) = ck for a large variety of planar graph problems. The key to this type of algorithm is what we call the "Layerwise Separation Property" of a planar graph problem. Problems having this property include PLANAR VERTEX COVER, PLANAR INDEPENDENT SET, AND PLANAR DOMINATING SET.

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