Randomized Online Algorithms for Set Cover Leasing Problems

Combinatorial Optimization and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-319-12691-3_3 ◽

2014 ◽

pp. 25-34 ◽

Cited By ~ 7

Author(s):

Sebastian Abshoff ◽

Christine Markarian ◽

Friedhelm Meyer auf der Heide

Keyword(s):

Online Algorithms ◽

Set Cover

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Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

Proceedings of the 22nd ACM symposium on Parallelism in algorithms and architectures - SPAA '10 ◽

10.1145/1810479.1810533 ◽

2010 ◽

Cited By ~ 17

Author(s):

Matti Åstrand ◽

Jukka Suomela

Keyword(s):

Approximation Algorithms ◽

Vertex Cover ◽

Set Cover ◽

Anonymous Networks ◽

Distributed Approximation

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Online Algorithms for Optimizing Age of Information in the IoT Systems with Multi-Slot Status Delivery

IEEE Wireless Communications Letters ◽

10.1109/lwc.2021.3052569 ◽

2021 ◽

Vol 10 (5) ◽

pp. 971-975

Author(s):

Xin Xie ◽

Heng Wang ◽

Lei Yu ◽

Mingjiang Weng

Keyword(s):

Online Algorithms ◽

Age Of Information

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SIGACT News Online Algorithms Column 37

ACM SIGACT News ◽

10.1145/3471469.3471480 ◽

2021 ◽

Vol 52 (2) ◽

pp. 71-71

Author(s):

Rob van Stee

Keyword(s):

Lower Bound ◽

Online Algorithms ◽

Packet Scheduling ◽

Open Problems ◽

Competitive Algorithm ◽

Long Time ◽

News Online

For this issue, Pavel Vesely has contributed a wonderful overview of the ideas that were used in his SODA paper on packet scheduling with Marek Chrobak, Lukasz Jez and Jiri Sgall. This is a problem for which a 2-competitive algorithm as well as a lower bound of ϕ ≈ 1:618 was known already twenty years ago, but which resisted resolution for a long time. It is great that this problem has nally been resolved and that Pavel was willing to explain more of the ideas behind it for this column. He also provides an overview of open problems in this area.

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SIGACT News Online Algorithms Column 28

ACM SIGACT News ◽

10.1145/2951860.2951871 ◽

2016 ◽

Vol 47 (2) ◽

pp. 40-51 ◽

Cited By ~ 3

Author(s):

Rob van Stee

Keyword(s):

Online Algorithms ◽

News Online

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PE-MSC: partial entailment-based minimum set cover for text summarization

Knowledge and Information Systems ◽

10.1007/s10115-020-01537-1 ◽

2021 ◽

Author(s):

Anand Gupta ◽

Manpreet Kaur ◽

Sonaali Mittal ◽

Swati Garg

Keyword(s):

Text Summarization ◽

Set Cover

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Competitive Caching with Machine Learned Advice

Journal of the ACM ◽

10.1145/3447579 ◽

2021 ◽

Vol 68 (4) ◽

pp. 1-25

Author(s):

Thodoris Lykouris ◽

Sergei Vassilvitskii

Keyword(s):

Online Algorithms ◽

Empirical Evaluation ◽

Optimal Solution ◽

Poor Performance ◽

Machine Learning Algorithms ◽

Average Error ◽

Generalization Error ◽

Worst Case ◽

Future Events ◽

Real World Datasets

Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution, as compared to an offline optimum. On the other hand, machine learning algorithms are in the business of extrapolating patterns found in the data to predict the future, and usually come with strong guarantees on the expected generalization error. In this work, we develop a framework for augmenting online algorithms with a machine learned predictor to achieve competitive ratios that provably improve upon unconditional worst-case lower bounds when the predictor has low error. Our approach treats the predictor as a complete black box and is not dependent on its inner workings or the exact distribution of its errors. We apply this framework to the traditional caching problem—creating an eviction strategy for a cache of size k . We demonstrate that naively following the oracle’s recommendations may lead to very poor performance, even when the average error is quite low. Instead, we show how to modify the Marker algorithm to take into account the predictions and prove that this combined approach achieves a competitive ratio that both (i) decreases as the predictor’s error decreases and (ii) is always capped by O (log k ), which can be achieved without any assistance from the predictor. We complement our results with an empirical evaluation of our algorithm on real-world datasets and show that it performs well empirically even when using simple off-the-shelf predictions.

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