Optimal non-adaptive algorithm for edge estimation
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914199920181248 |
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| author | Bishnu, Arijit Chanda, Debarshi Das, Buddha Dev Ghosh, Arijit Mishra, Gopinath |
| author_facet | Bishnu, Arijit Chanda, Debarshi Das, Buddha Dev Ghosh, Arijit Mishra, Gopinath |
| contents | We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph, our method requires only $\widetilde{O}(\sqrt{n})$ queries, achieving sublinear query complexity. The algorithm independently samples a set of vertices and queries their degrees, and also independently samples a set of edges, using the answers to these queries to estimate the total number of edges in the graph. We further prove a matching lower bound, establishing the optimality of our algorithm and resolving the non-adaptive query complexity of this problem with respect to degree and random-edge queries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal non-adaptive algorithm for edge estimation Bishnu, Arijit Chanda, Debarshi Das, Buddha Dev Ghosh, Arijit Mishra, Gopinath Data Structures and Algorithms Combinatorics 68W20, 68Q25, 60C05 F.2.2 We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph, our method requires only $\widetilde{O}(\sqrt{n})$ queries, achieving sublinear query complexity. The algorithm independently samples a set of vertices and queries their degrees, and also independently samples a set of edges, using the answers to these queries to estimate the total number of edges in the graph. We further prove a matching lower bound, establishing the optimality of our algorithm and resolving the non-adaptive query complexity of this problem with respect to degree and random-edge queries. |
| title | Optimal non-adaptive algorithm for edge estimation |
| topic | Data Structures and Algorithms Combinatorics 68W20, 68Q25, 60C05 F.2.2 |
| url | https://arxiv.org/abs/2512.11994 |