Online Algorithms with Advice

Boyar, Joan; Favrholdt, Lene M.; Kudahl, Christian; Larsen, Kim S.; Mikkelsen, Jesper W.

doi:10.1145/3056461

Cited by 43 publications

(13 citation statements)

References 69 publications

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“…Another model for augmenting online algorithms, but not directly related to the prediction setting studied in this paper, is that of advice complexity, where information about the future is obtained in the form of some always correct bits of advice (see Boyar et al, 2017, for a survey). Emek et al (2011) considered MTS under advice complexity, andAngelopoulos et al (2020) consider advice complexity with possibly adversarial advice and focus on Pareto-optimal algorithms for consistency and robustness in several similar online problems.…”

Section: Related Workmentioning

confidence: 99%

Online metric algorithms with untrusted predictions

Antoniadis¹,

Coester²,

Eliáš³

et al. 2020

Preprint

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Machine-learned predictors, although achieving very good results for inputs resembling training data, cannot possibly provide perfect predictions in all situations. Still, decisionmaking systems that are based on such predictors need not only to benefit from good predictions but also to achieve a decent performance when the predictions are inadequate. In this paper, we propose a prediction setup for arbitrary metrical task systems (MTS) (e.g., caching, k-server and convex body chasing) and online matching on the line. We utilize results from the theory of online algorithms to show how to make the setup robust. Specifically for caching, we present an algorithm whose performance, as a function of the prediction error, is exponentially better than what is achievable for general MTS. Finally, we present an empirical evaluation of our methods on real world datasets, which suggests practicality.

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Section: Related Workmentioning

confidence: 99%

Online metric algorithms with untrusted predictions

Antoniadis¹,

Coester²,

Eliáš³

et al. 2020

Preprint

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“…在线算法族 {A ε } 称为在线问题的竞争比近似方案, 若对任意的 ε > 0, 算法 A ε 的竞争比至多为 (1 + ε)ρ * , 其中 ρ * 为该在线问题最好算法的竞争比. 随即 Chen 等 [124] 、Megow 和 Wiese [125] [126].…”

Section: 竞争比近似方案unclassified

“…并以此加工工件, 即可得到带建议的竞争比为 1 + ε 的在线算法. 另有一些半在线模型, 如缓冲, 目前还未找到用带建议的算法实现的途径 (参见文献[126]). 当然, 也有一些建议无法在现有半在线框架下解释.…”

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Online scheduling on parallel machines: A survey

Ling¹,

Tan²

2020

Sci. Sin.-Math.

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关键词排序在线竞争比 MSC (2010) 主题分类 90B35, 90C27 1 引言在线问题 (online problem) 是 20 世纪 80 年代起逐渐形成的一个新的研究方向, 可用于求解在线问题的算法称为在线算法 (online algorithm). 在线的两个基本特征是实例信息随算法执行过程逐渐披露、以及算法决策不可因后续出现的信息而更改. 相应地, 实例信息在算法执行前全部已知的问题称为离线问题 (offline problem). 在线问题及算法可抽象为在算法设计者和对手 (adversary) 之间进行的一个需求-应答博弈 (request-answer game). 对手每给出一个需求, 算法根据此前双方的应对和当前需求决定如何应答, 而对手再根据至目前为止双方的应对给出下一个需求. 算法的目标是使其性能尽可能好, 而对手的目标则恰好相反. 为对一个在线算法求解在线问题的性能作出定量的评估, 最坏情况比被移植到在线问题的研究中, 并结合其特点称其为竞争比 (competitive ratio). 称 ρ = inf{r 1 | C A (I) rC * (I), ∀ I} (ρ = inf{r 1 | C * (I) rC A (I), ∀ I})

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“…The advice complexity is the number of bits of advice that are sufficient and necessary for an online algorithm to solve the problem exactly. This is a research topic that has gained substantial attention; see [6] for a survey.…”

Section: Introductionmentioning

confidence: 99%

Query-competitive sorting with uncertainty

Halldórsson

Lima

2021

Theoretical Computer Science

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We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields: (i) a 3/2query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2 + O(1/k) if the components obtained have size at least k; (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also show that the advice complexity of the adaptive problem is n/2 if no error threshold is allowed, and n/3 • lg 3 for the general case.

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Online Algorithms with Advice

Cited by 43 publications

References 69 publications

Online metric algorithms with untrusted predictions

Online metric algorithms with untrusted predictions

Online scheduling on parallel machines: A survey

Query-competitive sorting with uncertainty

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