Papers › A Faster Algorithm for Maximum Weight Matching on Unrestricted Bipartite Graphs
A Faster Algorithm for Maximum Weight Matching on Unrestricted Bipartite Graphs
Shawxing Kwok
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Given a weighted bipartite graph G = (L, R, E, w), the maximum weight matching (MWM) problem seeks to find a matching M ⊆E that maximizes the total weight ∑_(e ∈M) w(e). This paper presents a novel algorithm with a time complexity of O(min(X³ + E, XE + X²logX)), 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 + V²logV), or more strictly O(XE + XVlogV), where V = L ∪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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections