Almost tight bounds for online hypergraph matching

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Letters Pub Date : 2024-07-01 DOI:10.1016/j.orl.2024.107143

Thorben Tröbst , Rajan Udwani

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Abstract

In the online hypergraph matching problem, hyperedges of size k over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A naïve greedy algorithm for this problem achieves a competitive ratio of $\frac{1}{k}$ . We show that no (randomized) online algorithm has competitive ratio better than $\frac{2 + o (1)}{k}$ . If edges are allowed to be assigned fractionally, we give a deterministic online algorithm with competitive ratio $\frac{1 - o (1)}{\ln (k)}$ and show that no online algorithm can have competitive ratio strictly better than $\frac{1 + o (1)}{\ln (k)}$ . Lastly, we give a $\frac{1 - o (1)}{\ln (k)}$ competitive algorithm for the fractional edge-weighted version of the problem under a free disposal assumption.

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在线超图匹配的近似紧约束

在联机超图匹配问题中，大小超过共同地集的超门以对抗顺序联机到达。目标是获得最大匹配（超图的不相交集合）。针对这个问题的一种天真贪婪算法的竞争比为......我们证明，没有一种（随机）在线算法的竞争比优于......如果允许以分数方式分配边，我们给出了一种具有竞争比的确定性在线算法，并证明没有一种在线算法的竞争比严格优于......最后，我们给出了在自由处置假设下该问题分数版本的竞争算法。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.