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.
@InProceedings{chakrabarty_et_al:LIPIcs.FSTTCS.2024.16, author = {Chakrabarty, Deeparnab and Liao, Hang}, title = {{Learning Partitions Using Rank Queries}}, booktitle = {44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)}, pages = {16:1--16:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-355-3}, ISSN = {1868-8969}, year = {2024}, volume = {323}, editor = {Barman, Siddharth and Lasota, S{\l}awomir}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.16}, URN = {urn:nbn:de:0030-drops-222051}, doi = {10.4230/LIPIcs.FSTTCS.2024.16}, annote = {Keywords: Query Complexity, Hypergraph Learning, Matroids} }
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