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arXiv · 1711.00599

Optimal Parametric Search for Path and Tree Partitioning

Greg N. Frederickson·Samson Zhou
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Abstract

We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices, removing $k$ edges to minimize the maximum-weight component. The algorithms use the parametric search paradigm, testing candidate values until an optimum is found while simultaneously reducing the running time needed for each test. For path-partitioning, the algorithm employs a synthetic weighting scheme that results in a constant fraction reduction in running time after each test. For tree-partitioning, our dual-pronged strategy makes progress no matter what the specific structure of our tree is.

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Greg N. Frederickson, Samson Zhou. 2017-11-02. Optimal Parametric Search for Path and Tree Partitioning. https://arxiv.org/abs/1711.00599

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