Summary: Improved Bounds for On­line Load Balancing
Matthew Andrews \Lambda
andrews@math.mit.edu
Michel X. Goemans y
goemans@math.mit.edu
Lisa Zhang z
ylz@math.mit.edu
Department of Mathematics, MIT.
Abstract
We consider the following load balancing problem. Jobs arrive on­line and must be assigned
to one of m machines thereby increasing the load on that machine by a certain weight. Jobs
also depart on­line. The goal is to minimize the maximum load on any machine, the load being
defined as the sum of the weights of the jobs assigned to the machine. The scheduler has also the
option of preempting a job and reassigning it to another machine. Whenever a job is assigned
or reassigned to a machine, the on­line algorithm incurs a reassignment cost depending on the
job. For arbitrary reassignment costs, we present an on­line algorithm with a competitive ratio
of 3:5981 against current load, i.e. the maximum load at any time is less than 3:5981 times the
lowest achievable load at that time. Our algorithm also incurs a reassignment cost less than
6:8285 times the cost of assigning all the jobs. This is the first algorithm with a constant bound
both on the competitive ratio and on the reassignment factor. For the special cases in which

Source: Andrews, Matthew - Mathematics of Networks and Systems, Mathematical Sciences Research Center, Bell Laboratories

Collections: Mathematics; Computer Technologies and Information Sciences