Prophet upper bounds for online matching and auctions

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2025-04-07 DOI:10.1016/j.orl.2025.107294

José A. Soto , Victor Verdugo

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引用次数: 0

Abstract

In the online 2-bounded auction problem, we have a collection of items represented as nodes in a graph and bundles of size two represented by edges. Agents are presented sequentially, each with a random weight function over the bundles. The goal of the decision-maker is to find an allocation of bundles to agents of maximum weight so that every item is assigned at most once, i.e., the solution is a matching in the graph. When the agents are single-minded (i.e., put all the weight in a single bundle), we recover the maximum weight prophet matching problem under edge arrivals (a.k.a. prophet matching).

In this work, we provide new and improved upper bounds on the competitiveness achievable by an algorithm for the general online 2-bounded auction and the (single-minded) prophet matching problems. For the adversarial arrival order of the agents, we show that no algorithm for the online 2-bounded auction problem achieves a competitiveness larger than 4/11, while no algorithm for prophet matching achieves a competitiveness larger than ≈0.4189. Using a continuous-time analysis, we also improve the known bounds for online 2-bounded auctions for random order arrivals to ≈0.5968 in the general case, a bound of ≈0.6867 in the IID model, and ≈0.6714 in prophet-secretary model.

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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.