Work

Flow time scheduling and prefix Beck-Fiala

Year: 2022

Type: conference-paper

Abstract: We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix Beck-Fiala (bounded ℓ1-norm) setting to bounds on the flow time of an optimal schedule. Combining our reduction with a deep result proved by Banaszczyk via convex geometry, give guarantees of O(√logn) and O(√logn logP) for max flow time and total flow time, respectively, improving upon the previous best guarantees of O(logn) and O(logn logP). Apart from the improved guarantees, the reduction motivates seemingly easy versions of prefix discrepancy questions: any constant bound on prefix Beck-Fiala where vectors have sparsity two (sparsity one being trivial) would already yield tight guarantees for both max flow time and total flow time. While known techniques solve this case when the entries take values in {−1,0,1}, we show that they are unlikely to transfer to the more general 2-sparse case of bounded ℓ1-norm.

Source: ACM SIGACT Symposium on Theory of Computing (STOC)

DOI: 10.1145/3519935.3520077

Authors: Nikhil Bansal, Lars Rohwedder, Ola Svensson

Institutions: University of Michigan, Maastricht University, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Scheduling and Optimization Algorithms

Subfield: Industrial and Manufacturing Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Award: Continuous Methods in Discrete Optimization