Covering selfish machines
  We consider the machine covering problem for selfish related machines. 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 (the previous best result 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.   Our paper presents the first results for this problem in the context of selfish machines. 
Leah Epstein and Rob van Stee