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Clustering with an oracle

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2016Publisher:IEEEJournal:2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Authors: Arya Mazumdar; Barna Saha;

doi: 10.1109/allerton.2016.7852305

Clustering with an oracle

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Abstract

Suppose, we are given V = {1, 2, …, n} ≡ [n], a set of n points, that can be clustered into k parts V i , i = 1, …, k; V i ∩ V j = ∅, ∀i ≠ j; the subsets V i ⊂ [n] and k are unknown to us. There is an oracle that can answer any pair-wise queries V × V → {±1}, where a query answer of +1 for (u, v) ∈ V ×V indicates u and v belong to the same cluster, and −1 indicates they do not. How many such queries are necessary and/or sufficient to find the clusters exactly?

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University of Massachusetts Amherst
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