Online Algorithms for Covering and Packing Problems with Convex Objectives

Comparing online algorithms for bin packing problems

Journal of Scheduling ◽

10.1007/s10951-009-0129-5 ◽

2009 ◽

Vol 15 (1) ◽

pp. 13-21 ◽

Cited By ~ 15

Author(s):

Leah Epstein ◽

Lene M. Favrholdt ◽

Jens S. Kohrt

Keyword(s):

Online Algorithms ◽

Bin Packing ◽

Packing Problems

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Optimal Online Algorithms for Multidimensional Packing Problems

SIAM Journal on Computing ◽

10.1137/s0097539705446895 ◽

2005 ◽

Vol 35 (2) ◽

pp. 431-448 ◽

Cited By ~ 32

Author(s):

Leah Epstein ◽

Rob van Stee

Keyword(s):

Online Algorithms ◽

Packing Problems

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Robust Online Algorithms for Certain Dynamic Packing Problems

Approximation and Online Algorithms - Lecture Notes in Computer Science ◽

10.1007/978-3-030-39479-0_4 ◽

2020 ◽

pp. 43-59

Author(s):

Sebastian Berndt ◽

Valentin Dreismann ◽

Kilian Grage ◽

Klaus Jansen ◽

Ingmar Knof

Keyword(s):

Online Algorithms ◽

Packing Problems

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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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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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Empowering the configuration-IP: new PTAS results for scheduling with setup times

Mathematical Programming ◽

10.1007/s10107-021-01694-3 ◽

2021 ◽

Author(s):

Klaus Jansen ◽

Kim-Manuel Klein ◽

Marten Maack ◽

Malin Rau

Keyword(s):

Approximation Scheme ◽

Constant Factor ◽

Setup Times ◽

Linear Programs ◽

Scheduling Problems ◽

Design Of Algorithms ◽

Packing Problems ◽

Integer Linear Programs ◽

One Machine ◽

Target Locations

AbstractInteger linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time $$f(1/\varepsilon )\cdot \mathrm {poly}(|I|)$$ f ( 1 / ε ) · poly ( | I | ) . Previously, only constant factor approximations of 5/3 and $$4/3 + \varepsilon $$ 4 / 3 + ε , respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.

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