Article ID Journal Published Year Pages File Type
418648 Discrete Applied Mathematics 2015 11 Pages PDF
Abstract

Ultrametrics   model the pairwise distances between living species, where the distance is measured by hereditary time. Reconstructing the tree from the ultrametric distance data is easy, but only if our data is exact. We consider the NP-complete problem of finding the closest ultrametric to noisy data, as modeled by multiplicative or additive total distortion, with or without a monotonicity assumption on the noise.We obtain approximation ratio O(logn)O(logn) for multiplicative distortion where nn is the number of species, and O(1+(ρ−1)−1)O(1+(ρ−1)−1) for additive distortion where ρρ is the minimum ratio of any two distinct input distances. As part of proving our approximation bound for additive distortion, we give the first constant-factor approximation algorithm for a previously-studied problem called Cluster Deletion.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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