Improved bounds for on-line load balancing

Abstract

We consider the following load balancing problem. Jobs arrive on-line and must be assigned to one of m machines thereby increasing the load on that machine by a certain weight. Jobs also depart on-line. 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 also has the option of preempting a job and reassigning it to another machine. Whenever a job is assigned or reassigned to a machine, the on-line algorithm incurs a reassignment cost depending on the job. For arbitrary reassignment costs, we present an on-line 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 the reassignment costs are either 1 or proportional to the weights, we present several algorithms which improve upon Westbrook's recent 6-competitive algorithm against current load. Our best competitive ratios are 3 + ε and 2 + ε for the unit and proportional cases respectively.

A longer version of this paper may be found on the World Wide Web at ftp://theory.lcs.mit.edu/pub/people/goemans/load.ps.

Supported by NSF contract 9302476-CCR and ARPA contract N00014-95-1-1246.

Supported by NSF contract 9302476-CCR, an NEC research grant and ARPA contract N00014-95-1-1246.

Supported by an NSF graduate fellowship and ARPA contract N00014-95-1-1246.