Abstract
Inspired by applications on search engines and web servers, we consider a load balancing problem with a general convex objective function. In this problem, we are given a bipartite graph on a set of sources S and a set of workers W and the goal is to distribute the load from each source among its neighboring workers such that the total load of workers are as balanced as possible. We present a new distributed algorithm that works with any symmetric nondecreasing convex function for evaluating the balancedness of the workers' load. Our algorithm computes a nearly optimal allocation of loads in O(log n log² d/ε³) rounds where n is the number of nodes, d is the maximum degree, and ε is the desired precision. If the objective is to minimize the maximum load, we modify the algorithm to obtain a nearly optimal solution in O(log n log d/ε²) rounds. This improves a line of algorithms that require a polynomial number of rounds in n and d and appear to encounter a fundamental barrier that prevents them from obtaining polylogarithmic runtime [Berenbrink et al., 2005; Berenbrink et al., 2009; Subramanian and Scherson, 1994; Rabani et al., 1998]. In our paper, we introduce a novel primaldual approach with multiplicative weight updates that allows us to circumvent this barrier. Our algorithm is inspired by [Agrawal et al., 2018] and other distributed algorithms for optimizing linear objectives but introduces several new twists to deal with general convex objectives.
BibTeX  Entry
@InProceedings{ahmadian_et_al:LIPIcs.ITCS.2021.79,
author = {Sara Ahmadian and Allen Liu and Binghui Peng and Morteza Zadimoghaddam},
title = {{Distributed Load Balancing: A New Framework and Improved Guarantees}},
booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
pages = {79:179:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771771},
ISSN = {18688969},
year = {2021},
volume = {185},
editor = {James R. Lee},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13618},
URN = {urn:nbn:de:0030drops136186},
doi = {10.4230/LIPIcs.ITCS.2021.79},
annote = {Keywords: Load balancing, Distributed algorithms}
}
Keywords: 

Load balancing, Distributed algorithms 
Collection: 

12th Innovations in Theoretical Computer Science Conference (ITCS 2021) 
Issue Date: 

2021 
Date of publication: 

04.02.2021 