Free access
Proceedings
Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

Dynamic Algorithms for Packing-Covering LPs via Multiplicative Weight Updates

Abstract

In the dynamic linear program (LP) problem, we are given an LP undergoing updates and we need to maintain an approximately optimal solution. Recently, significant attention (e.g. [Gupta et al. STOC'17; Arar et al. ICALP'18, Wajc STOC'20]) has been devoted to the study of special cases of dynamic packing and covering LPs, such as the dynamic fractional matching and set cover problems. But until now, there is no non-trivial dynamic algorithm for general packing and covering LPs.
In this paper, we settle the complexity of dynamic packing and covering LPs, up to a polylogarithmic factor in update time. More precisely, in the partially dynamic setting (where updates can either only relax or only restrict the feasible region), we give near-optimal deterministic ε-approximation algorithms with polylogarithmic amortized update time. Then, we show that both partially dynamic updates and amortized update time are necessary; without any of these conditions, the trivial algorithm that recomputes the solution from scratch after every update is essentially the best possible, assuming SETH.
To obtain our results, we initiate a systematic study of the multiplicative weights update (MWU) method in the dynamic setting. As by-products of our techniques, we also obtain the first online (1 + ε)-competitive algorithms for both covering and packing LPs with polylogarithmic recourse, and the first streaming algorithms for covering and packing LPs with linear space and polylogarithmic passes.

Formats available

You can view the full content in the following formats:

Information & Authors

Information

Published In

cover image Proceedings
Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)
Pages: 1 - 47
Editors: Nikhil Bansal, University of Michigan, Ann Arbor, Michigan, USA and Viswanath Nagarajan, University of Michigan, Ann Arbor, Michigan, USA
ISBN (Online): 978-1-61197-755-4

History

Published online: 16 January 2023

Authors

Affiliations

Sayan Bhattacharya
Thatchaphol Saranurak

Metrics & Citations

Metrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited By

There are no citations for this item

View Options

View options

PDF

View PDF

Get Access

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share on social media

On May 28, 2024, our site will enter Read Only mode for a limited time in order to complete a platform upgrade. As a result, the following functions will be temporarily unavailable: registering new user accounts, any updates to existing user accounts, access token activations, and shopping cart transactions. Contact [email protected] with any questions.