License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.7
URN: urn:nbn:de:0030-drops-175106
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17510/
Go to the corresponding LIPIcs Volume Portal

Assadi, Sepehr ; Bernstein, Aaron ; Langley, Zachary

All-Norm Load Balancing in Graph Streams via the Multiplicative Weights Update Method

pdf-format:
LIPIcs-ITCS-2023-7.pdf (0.8 MB)

Abstract

In the weighted load balancing problem, the input is an n-vertex bipartite graph between a set of clients and a set of servers, and each client comes with some nonnegative real weight. The output is an assignment that maps each client to one of its adjacent servers, and the load of a server is then the sum of the weights of the clients assigned to it. The goal is to find an assignment that is well-balanced, typically captured by (approximately) minimizing either the ?_∞- or ?₂-norm of the server loads. Generalizing both of these objectives, the all-norm load balancing problem asks for an assignment that approximately minimizes all ?_p-norm objectives for p ≥ 1, including p = ∞, simultaneously.
Our main result is a deterministic O(log n)-pass O(1)-approximation semi-streaming algorithm for the all-norm load balancing problem. Prior to our work, only an O(log n)-pass O(log n)-approximation algorithm for the ?_∞-norm objective was known in the semi-streaming setting.
Our algorithm uses a novel application of the multiplicative weights update method to a mixed covering/packing convex program for the all-norm load balancing problem involving an infinite number of constraints.

BibTeX - Entry

@InProceedings{assadi_et_al:LIPIcs.ITCS.2023.7,
  author =	{Assadi, Sepehr and Bernstein, Aaron and Langley, Zachary},
  title =	{{All-Norm Load Balancing in Graph Streams via the Multiplicative Weights Update Method}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17510},
  URN =		{urn:nbn:de:0030-drops-175106},
  doi =		{10.4230/LIPIcs.ITCS.2023.7},
  annote =	{Keywords: Load Balancing, Semi-Streaming Algorithms, Semi-Matching}
}

Keywords: Load Balancing, Semi-Streaming Algorithms, Semi-Matching
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI