Learning Partitions using Rank Queries
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914953381806080 |
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| author | Chakrabarty, Deeparnab Liao, Hang |
| author_facet | Chakrabarty, Deeparnab Liao, Hang |
| contents | 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 $O(n + k\log r)$-rank query algorithm for a general partition matroid where $k$ is the number of parts and $r$ is the rank of the matroid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Partitions using Rank Queries Chakrabarty, Deeparnab Liao, Hang Data Structures and Algorithms 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 $O(n + k\log r)$-rank query algorithm for a general partition matroid where $k$ is the number of parts and $r$ is the rank of the matroid. |
| title | Learning Partitions using Rank Queries |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.13092 |