Scheduling to minimize power consumption using submodular functions

Authors:
Erik D. Demaine;Morteza Zadimoghaddam
Affiliations:
MIT, Cambridge, MA, USA;MIT, Cambridge, MA, USA
Venue:
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Year:
2010

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Abstract

We develop logarithmic approximation algorithms for extremely general formulations of multiprocessor multi-interval offline task scheduling to minimize power usage. Here each processor has an arbitrary specified power consumption to be turned on for each possible time interval, and each job has a specified list of time interval/processor pairs during which it could be scheduled. (A processor need not be in use for an entire interval it is turned on.) If there is a feasible schedule, our algorithm finds a feasible schedule with total power usage within an O(log n) factor of optimal, where n is the number of jobs.(Even in a simple setting with one processor, the problem is Set-Cover hard.) If not all jobs can be scheduled and each job has a specified value, then our algorithm finds a schedule of value at least (1-ε) Z and power usage within an O(log(1/ε)) factor of the optimal schedule of value at least Z, for any specified Z and ε 0. At the foundation of our work is a general framework for logarithmic approximation to maximizing any submodular function subject to budget constraints.