Solving optimization problems with diseconomies of scale via decoupling

Konstantin Makarychev, Maxim Sviridenko

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

Abstract

We present a new framework for solving optimization problems with a diseconomy of scale. In such problems, our goal is to minimize the cost of resources used to perform a certain task. The cost of resources grows superlinearly, as xq, q ≥ 1, with the amount x of resources used. We define a novel linear programming relaxation for such problems, and then show that the integrality gap of the relaxation is Aq, where Aq is the q-th moment of the Poisson random variable with parameter 1. Using our framework, we obtain approximation algorithms for the Minimum Energy Efficient Routing, Minimum Degree Balanced Spanning Tree, Load Balancing on Unrelated Parallel Machines, and Unrelated Parallel Machine Scheduling with Nonlinear Functions of Completion Times problems. Our analysis relies on the decoupling inequality for nonnegative random variables. The inequality states that ||σn i=1 Xi||q ≤ Cq ||σni=1 Yi||q, where Xi are independent nonnegative random variables, Yi are possibly dependent nonnegative random variable, and each Yi has the same distribution as Xi. The inequality was proved by de la Pe;a in 1990. However, the optimal constant Cq was not known. We show that the optimal constant is Cq = Aq1/q.

Original languageEnglish (US)
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
PublisherIEEE Computer Society
Pages571-580
Number of pages10
ISBN (Electronic)9781479965175
DOIs
StatePublished - Dec 7 2014
Event55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 - Philadelphia, United States
Duration: Oct 18 2014Oct 21 2014

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Other

Other55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014
CountryUnited States
CityPhiladelphia
Period10/18/1410/21/14

ASJC Scopus subject areas

  • Computer Science(all)

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  • Cite this

    Makarychev, K., & Sviridenko, M. (2014). Solving optimization problems with diseconomies of scale via decoupling. In Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS (pp. 571-580). [6979042] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). IEEE Computer Society. https://doi.org/10.1109/FOCS.2014.67