TY - GEN

T1 - All-Norm Load Balancing in Graph Streams via the Multiplicative Weights Update Method

AU - Assadi, Sepehr

AU - Bernstein, Aaron

AU - Langley, Zachary

N1 - Publisher Copyright:
© Sepehr Assadi, Aaron Bernstein, and Zachary Langley; licensed under Creative Commons License CC-BY 4.0.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - 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 ℓ∞- or ℓ2-norm of the server loads. Generalizing both of these objectives, the all-norm load balancing problem asks for an assignment that approximately minimizes all ℓp-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 ℓ∞-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.

AB - 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 ℓ∞- or ℓ2-norm of the server loads. Generalizing both of these objectives, the all-norm load balancing problem asks for an assignment that approximately minimizes all ℓp-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 ℓ∞-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.

KW - Load Balancing

KW - Semi-Matching

KW - Semi-Streaming Algorithms

UR - http://www.scopus.com/inward/record.url?scp=85147545185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85147545185&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ITCS.2023.7

DO - 10.4230/LIPIcs.ITCS.2023.7

M3 - Conference contribution

AN - SCOPUS:85147545185

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 14th Innovations in Theoretical Computer Science Conference, ITCS 2023

A2 - Kalai, Yael Tauman

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 14th Innovations in Theoretical Computer Science Conference, ITCS 2023

Y2 - 10 January 2023 through 13 January 2023

ER -