Abstract
In the load balancing problem, the input is an nvertex bipartite graph G = (C ∪ S, E)  where the two sides of the bipartite graph are referred to as the clients and the servers  and a positive weight for each client c ∈ C. The algorithm must assign each client c ∈ C to an adjacent server s ∈ S. The load of a server is then the weighted sum of all the clients assigned to it. The goal is to compute an assignment that minimizes some function of the server loads, typically either the maximum server load (i.e., the 𝓁_∞norm) or the 𝓁_pnorm of the server loads. This problem has a variety of applications and has been widely studied under several different names, including: scheduling with restricted assignment, semimatching, and distributed backup placement.
We study load balancing in the distributed setting. There are two existing results in the CONGEST model. Czygrinow et al. [DISC 2012] showed a 2approximation for unweighted clients with roundcomplexity O(Δ⁵), where Δ is the maximum degree of the input graph. Halldórsson et al. [SPAA 2015] showed an O(log n / log log n)approximation for unweighted clients and O(log²n/log log n)approximation for weighted clients with roundcomplexity polylog(n).
In this paper, we show the first distributed algorithms to compute an O(1)approximation to the load balancing problem in polylog(n) rounds:
 In the CONGEST model, we give an O(1)approximation algorithm in polylog(n) rounds for unweighted clients. For weighted clients, the approximation ratio is O(log{n}).
 In the less constrained LOCAL model, we give an O(1)approximation algorithm for weighted clients in polylog(n) rounds.
Our approach also has implications for the standard sequential setting in which we obtain the first O(1)approximation for this problem that runs in nearlinear time. A 2approximation is already known, but it requires solving a linear program and is hence much slower. Finally, we note that all of our results simultaneously approximate all 𝓁_pnorms, including the 𝓁_∞norm.
BibTeX  Entry
@InProceedings{assadi_et_al:LIPIcs:2020:13079,
author = {Sepehr Assadi and Aaron Bernstein and Zachary Langley},
title = {{Improved Bounds for Distributed Load Balancing}},
booktitle = {34th International Symposium on Distributed Computing (DISC 2020)},
pages = {1:11:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771689},
ISSN = {18688969},
year = {2020},
volume = {179},
editor = {Hagit Attiya},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13079},
URN = {urn:nbn:de:0030drops130798},
doi = {10.4230/LIPIcs.DISC.2020.1},
annote = {Keywords: Load Balancing, Distributed Algorithms, Matching, SemiMatching}
}
Keywords: 

Load Balancing, Distributed Algorithms, Matching, SemiMatching 
Collection: 

34th International Symposium on Distributed Computing (DISC 2020) 
Issue Date: 

2020 
Date of publication: 

07.10.2020 