发表机构
CNRS, DIENS, PSL; Kyoto University（法国国家科学研究中心、信息系研究所、巴黎文理研究大学; 京都大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于拍卖的拟阵交框架，实现秩预言机模型下近线性查询复杂度的$(1-\u03b5)$近似算法，并首次获得常数遍半流式及确定性离线算法。
AI 中文摘要
在本文中，我们为拟阵交问题开发了一种新的基于拍卖的框架，并利用该框架在多种计算环境下获得了改进的近似算法。我们的框架受到Fleiner的广义稳定匹配算法的启发，并扩展了Assadi、Liu和Tarjan提出的用于二分匹配的半流式拍卖算法。利用该框架，对于任意$\u03b5>0$，我们在秩预言机模型中提出了一种简单的$(1-\u03b5)$近似算法，其查询复杂度与当前最快的算法相匹配。此外，通过扩展这一结果，我们首次获得了加权问题的$(1-\u03b5)$近似算法，该算法仅需要近线性数量的秩预言机查询，达到了该问题已知最佳的秩预言机查询复杂度。我们还在多遍流式模型中获得了拟阵交的$(1-\u03b5)$近似半流式算法，其中地面集的元素按顺序到达。这是第一个使用常数遍数且空间在拟阵秩上近线性的算法达到该近似比。当在标准离线环境中看待时，同一算法产生了第一个确定性的$(1-\u03b5)$近似算法，用于拟阵交问题，仅需要近线性数量的独立性预言机查询。
英文摘要
In this paper, we develop a new auction-based framework for matroid intersection and use it to obtain improved approximation algorithms in several computational settings. Our framework is inspired by Fleiner's generalized stable matching algorithm and extends the semi-streaming auction algorithm for bipartite matching due to Assadi, Liu, and Tarjan. Using this framework, for any $\varepsilon > 0$, we present a simple $(1-\varepsilon)$-approximation algorithm in the rank-oracle model whose query complexity matches that of the current fastest algorithm. Furthermore, by extending this result, we obtain the first $(1-\varepsilon)$-approximation algorithm for the weighted problem that requires only a near-linear number of rank-oracle queries, achieving the best known rank-oracle query complexity for the problem. We also obtain a $(1-\varepsilon)$-approximation semi-streaming algorithm for matroid intersection in the multi-pass streaming model, where the elements of the ground set arrive sequentially. It is the first algorithm achieving this approximation ratio using a constant number of passes and nearly linear space in the ranks of the matroids. When viewed in the standard offline setting, the same algorithm yields the first deterministic $(1-\varepsilon)$-approximation algorithm for matroid intersection that requires only a near-linear number of independence-oracle queries.
