 
Summary: Constant Factor Bounds for Online Load Balancing
on Related Machines
Matthew Andrews \Lambda
Abstract
We present the first algorithm for online load balancing on related machines which has a
constant competitive ratio against current load and a constant reassignment factor. Jobs arrive
in and depart from a system of machines online. Each job must be assigned to one of the
machines. The load on a machine is defined to be the sum of the weights of the jobs on that
machine divided by its capacity. A job may be reassigned but a reassignment cost which depends
on the job is incurred. Our algorithm has a competitive ratio of 32 and a reassignment factor of
79.5, i.e. at any time the maximum load is at most 32 times the lowest achievable load at that
time and the total reassignment cost incurred is at most 79.5 times the cost of assigning all the
jobs.
1 Introduction
We consider the following online load balancing problem for a system of m machines. Jobs arrive
in and depart from the system online. When a job arrives the scheduler assigns it to one of the
machines. We assume that the machines are related, i.e. each job has an associated weight and
each machine has an associated capacity. The load on a machine is the sum of the weights of jobs
on that machine divided by the machine capacity. At each point in time we aim to minimize the
maximum load on a machine. The scheduler is allowed to carry out job reassignments (also known
