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arXiv · 2610.00920

A Faster Auction Algorithm for Weighted Matroid Intersection

Tatsuya Terao
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Abstract

We consider the weighted matroid intersection problem in the independence-oracle model. A sequence of works by Huang--Kakimura--Kamiyama [SODA'16 \& Math. Program'19], Chekuri--Quanrud [SODA'16], Quanrud [ICALP'24], and Dudeja--Grilnberger [IPCO'26] has developed efficient $(1-\varepsilon)$-approximation algorithms for this problem. We present a simple deterministic auction algorithm that, given two matroids on a common ground set of size $n$, computes a $(1-\varepsilon)$-approximate maximum-weight common independent set using $O(n \varepsilon^{-2} \log^2(n))$ independence-oracle queries. This is the first deterministic $(1-\varepsilon)$-approximation algorithm for the weighted matroid intersection problem whose query complexity is nearly linear in $n$ and polynomial in $1/\varepsilon$. Our algorithm builds on the auction algorithm for unweighted matroid intersection by Huang--Kobayashi ['26], together with the analysis of the auction algorithm for weighted bipartite matching by Liu--Ke--Khuller [APPROX'23].

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Tatsuya Terao. 2026-10-01. A Faster Auction Algorithm for Weighted Matroid Intersection. https://arxiv.org/abs/2610.00920

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