Approximations for generalized unsplittable flow on paths with application to power systems optimization

Areg Karapetyan (), Khaled Elbassioni (), Majid Khonji () and Sid Chi-Kin Chau ()
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Areg Karapetyan: Khalifa University
Khaled Elbassioni: Khalifa University
Majid Khonji: Khalifa University
Sid Chi-Kin Chau: Australian National University

Annals of Operations Research, 2023, vol. 320, issue 1, No 7, 173-204

Abstract: Abstract The Unsplittable Flow on a Path (UFP) problem has garnered considerable attention as a challenging combinatorial optimization problem with notable practical implications. Steered by its pivotal applications in power engineering, the present work formulates a novel generalization of UFP, wherein demands and capacities in the input instance are monotone step functions over the set of edges. As an initial step towards tackling this generalization, we draw on and extend ideas from prior research to devise a quasi-polynomial time approximation scheme under the premise that the demands and capacities lie in a quasi-polynomial range. Second, retaining the same assumption, an efficient logarithmic approximation is introduced for the single-source variant of the problem. Finally, we round up the contributions by designing a (kind of) black-box reduction that, under some mild conditions, allows to translate LP-based approximation algorithms for the studied problem into their counterparts for the Alternating Current Optimal Power Flow problem—a fundamental workflow in operation and control of power systems.

Keywords: Unsplittable flow problem; QPTAS; LP rounding; Logarithmic approximation; Power systems engineering; AC optimal power flow (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-05054-y

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