在线匹配不允许\(o(\sqrt {\log n})\) -竞争算法

IF 0.9 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

ACM Transactions on Algorithms Pub Date : 2023-07-14 DOI:https://dl.acm.org/doi/10.1145/3594873

Enoch Peserico, Michele Scquizzato

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引用次数: 0

摘要

我们给出了一个简单的证明，对于任意n = 2i - 1: i∈n，没有任何随机在线匹配算法可以与遗忘对手\((\sqrt {\log _2(n+1)}/15)\)竞争。这是该问题的第一个超常数下界，并作为一个推论否定了最近关于在一般空间上可实现的拓扑参数化竞争的猜想。

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Matching on the Line Admits no \(o(\sqrt {\log n})\) -Competitive Algorithm

We present a simple proof that no randomized online matching algorithm for the line can be \((\sqrt {\log _2(n+1)}/15)\)-competitive against an oblivious adversary for any n = 2ⁱ - 1 : i ∈ ℕ. This is the first super-constant lower bound for the problem, and disproves as a corollary a recent conjecture on the topology-parametrized competitiveness achievable on generic spaces.

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来源期刊

ACM Transactions on Algorithms COMPUTER SCIENCE, THEORY & METHODS-MATHEMATICS, APPLIED

CiteScore

3.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ACM Transactions on Algorithms welcomes submissions of original research of the highest quality dealing with algorithms that are inherently discrete and finite, and having mathematical content in a natural way, either in the objective or in the analysis. Most welcome are new algorithms and data structures, new and improved analyses, and complexity results. Specific areas of computation covered by the journal include combinatorial searches and objects; counting; discrete optimization and approximation; randomization and quantum computation; parallel and distributed computation; algorithms for graphs, geometry, arithmetic, number theory, strings; on-line analysis; cryptography; coding; data compression; learning algorithms; methods of algorithmic analysis; discrete algorithms for application areas such as biology, economics, game theory, communication, computer systems and architecture, hardware design, scientific computing