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Microbiome in Idiopathic Pulmonary Fibrosis, it take to untangle ., i.e., to turn it into a simple polygon, if in each step we can arbitrarily relocate one of its vertices. It is shown that in some cases one has to move all but at most .((. log .).) vertices. On the other hand, every polygon . can be untangled in at most . steps. Some related questions are also considered.

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殺菌劑

Fast Compaction for Orthogonal Drawings with Vertices of Prescribed Sizeitical constraint for manypractical applications like UML. The algorithm provides a drastic improvement on previous approaches. It has linear worst case running time and experiments show that it performs veryw ell in practice.

discord

Untangling a Polygon it take to untangle ., i.e., to turn it into a simple polygon, if in each step we can arbitrarily relocate one of its vertices. It is shown that in some cases one has to move all but at most .((. log .).) vertices. On the other hand, every polygon . can be untangled in at most . steps. Some related questions are also considered.

Expiration

https://doi.org/10.1007/978-981-13-8495-0wires is equivalent to finding the drawing in which the edges are drawn as thick as possible. To the best of our knowledge this is the first algorithm that finds the maximal distance between any two wires and allows for wires of variable thickness. The previous best known result for the correspondin