Extra unit-speed machines are almost as powerful as speedy machines for competitive flow time scheduling

Abstract

We study online scheduling of jobs to minimize the flow time and stretch on parallel machines. We consider algorithms that are given extra resources so as to compensate the lack of future information. Recent results show that a modest increase in machine speed can provide very competitive performance; in particular, using O(1) times faster machines, the algorithm SRPT (shortest remaining processing time) is 1-competitive for both flow time [23] and stretch [12], and HDF (high-est density first) is O(1)-competitive for weighted flow time [6]. Using extra unit-speed machines instead of faster machines is more challenging. This paper gives a non-trivial relationship between the extra-speed and extra-machine analysis. It shows that competitive results via faster machines can be transformed to similar results via extra machines, and hence giving the first algorithms that, using O(1) times unit-speed machines, are 1-competitive for flow time and stretch and O(1)-competitive for weighted flow time, respectively.