Abstract
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 sum of vertex costs at most \(c\sqrt {\Sigma _{v \in V(G)} (cost(v))^2 }\) and that this bound is optimal to within a constant factor. Moreover such a separator can be found in linear time. This theorem implies a variety of other separation results. We describe applications of our separator theorems to graph embedding problems, to graph pebbling, and to multi-commodity flow problems.
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Djidjev, H.N. (1997). Weighted graph separators and their applications. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_11
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DOI: https://doi.org/10.1007/3-540-63397-9_11
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