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Learning Partitions Using Rank Queries

Authors Deeparnab Chakrabarty , Hang Liao

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Author Details

Deeparnab Chakrabarty
  • Dartmouth College, Hanover, NH, USA
Hang Liao
  • Dartmouth College, Hanover, NH, USA

Funding

  • Chakrabarty, Deeparnab: Supported by NSF grants 2041920 and 2402571.
  • Liao, Hang: Supported by NSF grant 2041920.

Cite As Get BibTex

Deeparnab Chakrabarty and Hang Liao. Learning Partitions Using Rank Queries. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FSTTCS.2024.16

Abstract

We consider the problem of learning an unknown partition of an n element universe using rank queries. Such queries take as input a subset of the universe and return the number of parts of the partition it intersects. We give a simple O(n)-query, efficient, deterministic algorithm for this problem. We also generalize to give an O(n + klog r)-rank query algorithm for a general partition matroid where k is the number of parts and r is the rank of the matroid.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Query Complexity
  • Hypergraph Learning
  • Matroids

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