A Simple $(1-ε)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching
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 $n$ -- w...
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| Published in: | TheoretiCS Vol. 4 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.08.2025
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| ISSN: | 2751-4838, 2751-4838 |
| Online Access: | Get full text |
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| Summary: | 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.
25 pages. This is the TheoretiCS journal version |
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| ISSN: | 2751-4838 2751-4838 |
| DOI: | 10.46298/theoretics.25.16 |