A Faster Algorithm for Maximum Weight Matching on Unrestricted Bipartite Graphs
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916673822392320 |
|---|---|
| author | Kwok, Shawxing |
| author_facet | Kwok, Shawxing |
| contents | Given a weighted bipartite graph $G = (L, R, E, w)$, the maximum weight matching (MWM) problem seeks to find a matching $M \subseteq E$ that maximizes the total weight $\sum_{e \in M} w(e)$.
This paper presents a novel algorithm with a time complexity of $O(\min(X^3 + E, XE + X^2\log X))$, where $X = \min(|L|, |R|)$. Unlike many existing algorithms, our approach supports real-valued weights without additional constraints. Under this condition, our result improves upon the previous best-known bound of $O(VE + V^2\log V)$, or more strictly $O(XE + XV\log V)$, where $V = L \cup R$.
The suggested implementation code is simplified and publicly available at https://github.com/ShawxingKwok/Kwok-algorithm, with the average-case time complexity of $O(E^{1.4} + LR)$ estimated from experimental results on random graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Faster Algorithm for Maximum Weight Matching on Unrestricted Bipartite Graphs Kwok, Shawxing Data Structures and Algorithms Given a weighted bipartite graph $G = (L, R, E, w)$, the maximum weight matching (MWM) problem seeks to find a matching $M \subseteq E$ that maximizes the total weight $\sum_{e \in M} w(e)$. This paper presents a novel algorithm with a time complexity of $O(\min(X^3 + E, XE + X^2\log X))$, where $X = \min(|L|, |R|)$. Unlike many existing algorithms, our approach supports real-valued weights without additional constraints. Under this condition, our result improves upon the previous best-known bound of $O(VE + V^2\log V)$, or more strictly $O(XE + XV\log V)$, where $V = L \cup R$. The suggested implementation code is simplified and publicly available at https://github.com/ShawxingKwok/Kwok-algorithm, with the average-case time complexity of $O(E^{1.4} + LR)$ estimated from experimental results on random graphs. |
| title | A Faster Algorithm for Maximum Weight Matching on Unrestricted Bipartite Graphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2502.20889 |