Weighted Online Problems with Advice

Weighted Online Problems with Advice Recently, the first online complexity class, A O C, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solution. All A O C-complete problems (including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have essentially the same advice complexity. In this paper, we study weighted versions of problems in A O C, i.e., each request comes with a weight and the aim is to either minimize or maximize the total weight of the accepted requests. In contrast to the unweighted versions, we show that there is a significant difference in the advice complexity of complete minimization and maximization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete A O C problems such as Matching in the edge arrival model (giving better results than what follow from the general A O C results) and even non- A O C problems such as scheduling. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

Weighted Online Problems with Advice

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
D.O.I.
10.1007/s00224-017-9806-5
Publisher site
See Article on Publisher Site

Abstract

Recently, the first online complexity class, A O C, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solution. All A O C-complete problems (including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have essentially the same advice complexity. In this paper, we study weighted versions of problems in A O C, i.e., each request comes with a weight and the aim is to either minimize or maximize the total weight of the accepted requests. In contrast to the unweighted versions, we show that there is a significant difference in the advice complexity of complete minimization and maximization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete A O C problems such as Matching in the edge arrival model (giving better results than what follow from the general A O C results) and even non- A O C problems such as scheduling.

Journal

Theory of Computing SystemsSpringer Journals

Published: Sep 19, 2017

References

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