Approximating weighted completion time via stronger negative correlation

Alok Baveja (), Xiaoran Qu () and Aravind Srinivasan ()
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Alok Baveja: Rutgers Business School
Xiaoran Qu: Department of Electrical Engineering and Computer Science
Aravind Srinivasan: University of Maryland

Journal of Scheduling, 2024, vol. 27, issue 4, No 1, 319-328

Abstract: Abstract Minimizing the weighted completion time of jobs in the unrelated parallel machines model is a fundamental scheduling problem. The first $$(3/2 - c)$$ ( 3 / 2 - c ) –approximation algorithm for this problem, for some constant $$c > 0$$ c > 0 , was obtained in the work of Bansal et al. (SIAM J Comput, 2021). A key ingredient in this work was the first dependent-rounding algorithm with a certain guaranteed amount of negative correlation. We improve upon this guaranteed amount from 1/108 to 1/27, thus also improving upon the constant c in the algorithms of Bansal et al. and Li (SIAM J Comput, 2020) for weighted completion time. Given the now-ubiquitous role played by dependent rounding in scheduling and combinatorial optimization, our improved dependent rounding is also of independent interest.

Keywords: Scheduling; Completion time; Approximation algorithms; Dependent rounding; 68Q25; 68Q87; 90B35 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10951-023-00780-y

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