Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913206183657472 |
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| author | Zheng, Da Wei Henzinger, Monika |
| author_facet | Zheng, Da Wei Henzinger, Monika |
| contents | $\newcommand{\eps}{\varepsilon}$We present an auction algorithm using multiplicative instead of constant weight updates to compute a $(1-\eps)$-approximate maximum weight matching (MWM) in a bipartite graph with $n$ vertices and $m$ edges in time $O(m\eps^{-1})$, beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM '14] that runs in $O(m\eps^{-1}\log \eps^{-1})$. Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a $(1-\eps)$-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time used is $O(m\eps^{-1})$, where $m$ is the sum of the number of initially existing and inserted edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09217 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching Zheng, Da Wei Henzinger, Monika Data Structures and Algorithms $\newcommand{\eps}{\varepsilon}$We present an auction algorithm using multiplicative instead of constant weight updates to compute a $(1-\eps)$-approximate maximum weight matching (MWM) in a bipartite graph with $n$ vertices and $m$ edges in time $O(m\eps^{-1})$, beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM '14] that runs in $O(m\eps^{-1}\log \eps^{-1})$. Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a $(1-\eps)$-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time used is $O(m\eps^{-1})$, where $m$ is the sum of the number of initially existing and inserted edges. |
| title | Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2301.09217 |