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arXiv · 2004.13202

Learning Lines with Ordinal Constraints

Bohan Fan·Diego Ihara Centurion·Neshat Mohammadi·Francesco Sgherzi·Anastasios Sidiropoulos·Mina Valizadeh
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Abstract

We study the problem of finding a mapping $f$ from a set of points into the real line, under ordinal triple constraints. An ordinal constraint for a triple of points $(u,v,w)$ asserts that $|f(u)-f(v)|<|f(u)-f(w)|$. We present an approximation algorithm for the dense case of this problem. Given an instance that admits a solution that satisfies $(1-\varepsilon)$-fraction of all constraints, our algorithm computes a solution that satisfies $(1-O(\varepsilon^{1/8}))$-fraction of all constraints, in time $O(n^7) + (1/\varepsilon)^{O(1/\varepsilon^{1/8})} n$.

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Bohan Fan, Diego Ihara Centurion, Neshat Mohammadi, Francesco Sgherzi, Anastasios Sidiropoulos, Mina Valizadeh. 2020-04-27. Learning Lines with Ordinal Constraints. https://arxiv.org/abs/2004.13202

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