A Simple $(1-ε)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918114631876608 |
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| author | Assadi, Sepehr |
| author_facet | Assadi, Sepehr |
| contents | We present a simple semi-streaming algorithm for $(1-ε)$-approximation of bipartite matching in $O(\log{\!(n)}/ε)$ passes. This matches the performance of state-of-the-art "$ε$-efficient" algorithms -- the ones with much better dependence on $ε$ albeit with some mild dependence on $n$ -- while being considerably simpler.
The algorithm relies on a direct application of the multiplicative weight update method with a self-contained primal-dual analysis that can be of independent interest. To show case this, we use the same ideas, alongside standard tools from matching theory, to present an equally simple semi-streaming algorithm for $(1-ε)$-approximation of weighted matchings in general (not necessarily bipartite) graphs, again in $O(\log{\!(n)}/ε)$ passes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02968 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Simple $(1-ε)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching Assadi, Sepehr Data Structures and Algorithms Distributed, Parallel, and Cluster Computing We present a simple semi-streaming algorithm for $(1-ε)$-approximation of bipartite matching in $O(\log{\!(n)}/ε)$ passes. This matches the performance of state-of-the-art "$ε$-efficient" algorithms -- the ones with much better dependence on $ε$ albeit with some mild dependence on $n$ -- while being considerably simpler. The algorithm relies on a direct application of the multiplicative weight update method with a self-contained primal-dual analysis that can be of independent interest. To show case this, we use the same ideas, alongside standard tools from matching theory, to present an equally simple semi-streaming algorithm for $(1-ε)$-approximation of weighted matchings in general (not necessarily bipartite) graphs, again in $O(\log{\!(n)}/ε)$ passes. |
| title | A Simple $(1-ε)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching |
| topic | Data Structures and Algorithms Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2307.02968 |