Almost-Uniform Edge Sampling: Leveraging Independent-Set and Local Graph Queries
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918393322405888 |
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| author | Adar, Tomer Levi, Amit |
| author_facet | Adar, Tomer Levi, Amit |
| contents | A central theme in sublinear graph algorithms is the relationship between counting and sampling: can the ability to approximately count a combinatorial structure be leveraged to sample it nearly uniformly at essentially the same cost?
We study (i) independent-set (IS) queries, which return whether a vertex set $S$ is edge-free, and (ii) two standard local queries: degree and neighbor queries. Eden and Rosenbaum (SOSA `18) proved that in the local-query model, uniform edge sampling is no harder than approximate edge counting. We extend this phenomenon to new settings.
We establish sampling-counting equivalence for the hybrid model that combines IS and local queries, matching the complexity of edge-count estimation achieved by Adar, Hotam and Levi (2026), and an analogous equivalence for IS queries, matching the complexity of edge-count estimation achieved by Chen, Levi and Waingarten (SODA `20).
For each query model, we show lower bounds for uniform edge sampling that essentially coincide with the known bounds for approximate edge counting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Almost-Uniform Edge Sampling: Leveraging Independent-Set and Local Graph Queries Adar, Tomer Levi, Amit Data Structures and Algorithms A central theme in sublinear graph algorithms is the relationship between counting and sampling: can the ability to approximately count a combinatorial structure be leveraged to sample it nearly uniformly at essentially the same cost? We study (i) independent-set (IS) queries, which return whether a vertex set $S$ is edge-free, and (ii) two standard local queries: degree and neighbor queries. Eden and Rosenbaum (SOSA `18) proved that in the local-query model, uniform edge sampling is no harder than approximate edge counting. We extend this phenomenon to new settings. We establish sampling-counting equivalence for the hybrid model that combines IS and local queries, matching the complexity of edge-count estimation achieved by Adar, Hotam and Levi (2026), and an analogous equivalence for IS queries, matching the complexity of edge-count estimation achieved by Chen, Levi and Waingarten (SODA `20). For each query model, we show lower bounds for uniform edge sampling that essentially coincide with the known bounds for approximate edge counting. |
| title | Almost-Uniform Edge Sampling: Leveraging Independent-Set and Local Graph Queries |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2603.14306 |