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arXiv · 1504.04073

The Parametric Closure Problem

David Eppstein
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Abstract

We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights vary. We give polynomial time solutions to many important special cases of this problem including semiorders, reachability orders of bounded-treewidth graphs, partial orders of bounded width, and series-parallel partial orders. Our result for series-parallel orders provides a significant generalization of a previous result of Carlson and Eppstein on bicriterion subtree problems.

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David Eppstein. 2015-04-16. The Parametric Closure Problem. https://doi.org/10.1145/3147212

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