On Undecided LP, Clustering and Active Learning

Authors Stav Ashur , Sariel Har-Peled

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Stav Ashur
  • Department of Computer Science, University of Illinois, Urbana, IL, USA
Sariel Har-Peled
  • Department of Computer Science, University of Illinois, Urbana, IL, USA


The authors thank Pankaj Agarwal for useful discussions. We thank Lev Reyzin for pointing out the work by Maass and Turán [Maass and Tur{á}n, 1994; Maass and Turán, 1994].

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Stav Ashur and Sariel Har-Peled. On Undecided LP, Clustering and Active Learning. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We study colored coverage and clustering problems. Here, we are given a colored point set, where the points are covered by k (unknown) clusters, which are monochromatic (i.e., all the points covered by the same cluster have the same color). The access to the colors of the points (or even the points themselves) is provided indirectly via various oracle queries (such as nearest neighbor, or separation queries). We show that one can correctly deduce the color of all the points (i.e., compute a monochromatic clustering of the points) using a polylogarithmic number of queries, if the number of clusters is a constant. We investigate several variants of this problem, including Undecided Linear Programming and covering of points by k monochromatic balls.

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Linear Programming
  • Active learning
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