Paper by Erik D. Demaine
- Erik D. Demaine and Morteza Zadimoghaddam, “Scheduling to Minimize Power Consumption using Submodular Functions”, in Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2010), Santorini, Greece, June 13–15, 2010, pages 21–29.
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.
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- Related papers:
- GapScheduling_JScheduling (Scheduling to Minimize Gaps and Power Consumption)
- GapScheduling_SPAA2007 (Scheduling to Minimize Gaps and Power Consumption)
See also other papers by Erik Demaine.
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