Online mixed packing and covering

Yossi Azar*, Umang Bhaskar, Lisa Fleischer, Debmalya Panigrahi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Recent work has shown that the classical framework of solving optimization problems by obtaining a fractional solution to a linear program (LP) and rounding it to an integer solution can be extended to the online setting using primal-dual techniques. The success of this new framework for online optimization can be gauged from the fact that it has led to progress in several longstanding open questions. However, to the best of our knowledge, this framework has previously been applied to LPs containing only packing or only covering constraints, or minor variants of these. We extend this framework in a fundamental way by demonstrating that it can be used to solve mixed packing and covering LPs online, where packing constraints are given offline and covering constraints are received online. The objective is to minimize the maximum multiplicative factor by which any packing constraint is violated, while satisfying the covering constraints. Our results represent the first algorithm that obtains a polylogarithmic competitive ratio for solving mixed LPs online. We then consider two canonical examples of mixed LPs: unrelated machine scheduling with startup costs, and capacity constrained facility location. We use ideas generated from our result for mixed packing and covering to obtain polylogarithmic-competitive algorithms for these problems. We also give lower bounds to show that the competitive ratios of our algorithms are nearly tight.

Original languageEnglish
Title of host publicationProceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
PublisherAssociation for Computing Machinery
Number of pages16
ISBN (Print)9781611972511
StatePublished - 2013
Event24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 - New Orleans, LA, United States
Duration: 6 Jan 20138 Jan 2013

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
Country/TerritoryUnited States
CityNew Orleans, LA


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