Skeletons and Minimum Energy Scheduling
Consider the problem where n jobs, each with a release time, a deadline and a required processing time are to be feasibly scheduled in a single- or multi-processor setting so as to minimize the total energy consumption of the schedule. A processor has two available states: a sleep state where no energy is consumed but also no processing can take place, and an active state which consumes energy at a rate of one, and in which jobs can be processed. Transitioning from the active to the sleep does not incur any further energy cost, but transitioning from the sleep to the active state requires q energy units. Jobs may be preempted and (in the multi-processor case) migrated.
The single-processor case of the problem is known to be solvable in polynomial time via an involved dynamic program, whereas the only known approximation algorithm for the multi-processor case attains an approximation factor of 3 and is based on rounding the solution to a linear programming relaxation of the problem. In this work, we present efficient and combinatorial approximation algorithms for both the single- and the multi-processor setting. Before, only an algorithm based on linear programming was known for the multi-processor case. Our algorithms build upon the concept of a skeleton, a basic (and not necessarily feasible) schedule that captures the fact that some processor(s) must be active at some time point during an interval. Finally, we further demonstrate the power of skeletons by providing a 2-approximation algorithm for the multiprocessor case, thus improving upon the recent breakthrough 3-approximation result. Our algorithm is based on a novel rounding scheme of a linear-programming relaxation of the problem which incorporates skeletons.
scheduling
energy-efficiency
approximation algorithms
dynamic programming
combinatorial algorithms
Theory of computation~Scheduling algorithms
51:1-51:16
Regular Paper
https://arxiv.org/abs/2107.07800
Antonios
Antoniadis
Antonios Antoniadis
University of Twente, Enschede, The Netherlands
https://orcid.org/0000-0003-2152-7883
Gunjan
Kumar
Gunjan Kumar
National University of Singapore, Singapore
This work was supported in part by National Research Foundation Singapore under its NRF Fellowship Programme [NRF-NRFFAI1-2019-0004] and AI Singapore Programme [AISG-RP-2018-005], and NUS ODPRT Grant [R-252-000-685-13].
Nikhil
Kumar
Nikhil Kumar
Hasso Plattner Institute Potsdam, Germany
10.4230/LIPIcs.ISAAC.2021.51
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Antonios Antoniadis, Gunjan Kumar, and Nikhil Kumar
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