Maximizing the Minimum Load for Selfisch Agents

Abstract

We consider the problem of maximizing the minimum load for
machines that are controlled by selfish agents, who are only
interested in maximizing their own profit. Unlike the classical
load balancing problem, this problem 
has not been considered for selfish agents until now.

For a constant number of machines, $m$, we show a
monotone polynomial time approximation scheme (PTAS) with running
time that is linear in the number of jobs. It uses a new
technique for reducing the number of jobs while remaining close
to the optimal solution. We also present an FPTAS for the classical
machine covering problem, i.e., where no selfish agents are involved
(the previous best result for this case was a PTAS)
and use this to give a monotone FPTAS.

Additionally, we give a monotone approximation algorithm with
approximation ratio $min(m,(2+eps)s_1/s_m)$ where $eps>0$ can
be chosen arbitrarily small and $s_i$ is the (real) speed of
machine $i$. Finally we give improved results for two machines.