A coupled task scheduling approximation algorithm for minimizing the sum of completion times
Year: 2026
Type: article
Abstract: In the considered coupled task problem (CTP) we have to schedule n jobs on a single machine, each consisting of two tasks with exact time delay between them, while the objective is to minimize the total completion time of the jobs. We analyze a greedy type algorithm – called SDF (Shortest Delay First) – from worst case point of view, and we give bounds for the asymptotic behavior of SDF for the special case where each task has equal length processing time p . For this case, the best-known upper bound on the asymptotic performance ratio of algorithm SDF is $$\frac{5}{3}\approx 1.666\ldots .$$ 5 3 ≈ 1.666 … . We improve this bound to a general upper bound $$\frac{21p-\sqrt{3(43p^2-28p+4)}-6}{6p}$$ 21 p - 3 ( 43 p 2 - 28 p + 4 ) - 6 6 p that holds for all $$p\ge 2.$$ p ≥ 2 . Using constructions to compute lower bounds, we give narrow intervals for the asymptotic behavior of algorithm SDF as a function of the parameter p .
Source: Annals of Operations Research
Authors: József Békési, György Dósa, Gábor Galambos
Institutions: University of Szeged, University of Pannonia
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Szegedi Tudományegyetem
OpenAlex ID: W7161751691