 
Summary: Load balancing of temporary tasks in the # p norm
Yossi Azar # Amir Epstein + Leah Epstein #
Abstract
We consider the online load balancing problem where there are m identical machines (servers).
Jobs arrive at arbitrary times, where each job has a weight and a duration. A job has to be as
signed upon its arrival to exactly one of the machines. The duration of each job becomes known
only upon its termination (this is called temporary tasks of unknown durations). Once a job has
been assigned to a machine it cannot be reassigned to another machine. The goal is to minimize
the maximum over time of the sum (over all machines) of the squares of the loads, instead of the
traditional maximum load.
We show that for the sum of the squares the greedy algorithm performs within at most 2.23 of
the optimum. We show (an asymptotic) lower bound of 1.79 on the competitive ratio of the greedy
algorithm. We also show a lower bound of 1.44 on the competitive ratio of any deterministic
algorithm.
Minimizing the sum of the squares is equivalent to minimizing the load vector with respect to
the # 2 norm. We extend our techniques and analyze the competitive ratio of greedy with respect
to the # p norm. We show that the greedy algorithm performs within at most 2  # /p) of the
optimum. We also show a lower bound of 2  O(ln p/p) on the competitive ratio of any online
algorithm.
1 Introduction
