Improved bi-criteria approximation schemes for load balancing on unrelated machines with cost constraints

• Published in: Theoretical computer science Vol. 858; pp. 35 - 48
• Main Authors: Nguyen, Trung Thanh, Rothe, Jörg
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.02.2021
• Subjects: Bi-criteria approximation algorithm; Load balancing; Machine scheduling; Polynomial-time approximation algorithm; Machine scheduling; Load balancing; Bi-criteria approximation algorithm; Polynomial-time approximation algorithm
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2020.12.022

•We study a generalized version of the load balancing problem on unrelated machines with cost constraints.•We develop a bi-criteria approximation scheme for this problem.•We generalize known results for special cases (identical machines or a constant number of machines with cost constraints).•Our approach can be used to find approximation schemes for a wider class of load balancing problems with linear constraints. We study a generalized version of the load balancing problem on unrelated machines with cost constraints: Given a set of m machines (of certain types) and a set of n jobs, each job j processed on machine i requires pi,j time units and incurs a cost ci,j, and the goal is to find a schedule of jobs to machines, which is defined as an ordered partition of n jobs into m disjoint subsets, in such a way that some objective function of the vector of the completion times of the machines is optimized, subject to the constraint that the total costs by the schedule must be within a given budget B. Motivated by recent results from the literature, our focus is on the case when the number of machine types is a fixed constant and we develop a bi-criteria approximation scheme for the studied problem. Our result generalizes several known results for certain special cases, such as the case with identical machines, or the case with a constant number of machines with cost constraints. Building on the elegant technique recently proposed by Jansen and Maack [1], we construct a more general approach that can be used to derive approximation schemes for a wider class of load balancing problems with linear constraints.