Partitioning Graphs with Costs and Weights on Vertices: Algorithms and Applications
نویسنده
چکیده
We prove separator theorems in which the size of the separator is minimized with respect to non-negative vertex costs. We show that for any planar graph G there exists a vertex separator of total vertex cost at most c q P v2V (G) (cost(v)) 2 and that this bound is optimal within a constant factor. Moreover such a separator can be found in linear time. This theorem implies a variety of other separation results discussed in the paper. We describe application of our separator theorems to graph embedding problems, graph pebbling, and multi{ commodity ow problems.
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