New algorithms for coupled tasks scheduling – a survey

Abstract

The coupled tasks scheduling problem is a class of scheduling problems introduced for beam steering software of sophisticated radar devices, called phased arrays. Due to increasing popularity of such radars, the importance of coupled tasks scheduling is constantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, and only a few practically usable algorithms for such problems were found. This paper provides a survey of already known complexity results of various variants of coupled tasks problems. Then, it complements previous results by providing experimental results of two new polynomial algorithms for coupled tasks scheduling, which are: an exact algorithm for 1|(1, 4, 1), strict chains|Cmax problem, and a fast heuristic algorithm for more general 1|(1, 2k, 1), strict chains|Cmax problem, where k ∈ N.

Scheduling coupled tasks with exact delays for minimum total job completion time

“…Recently, Khatami et al (2020) provided an updated survey of research on scheduling coupled tasks with exact time delays. An earlier survey was given by Blazewicz et al (2012). We refer the reader to these two reviews for more details.…”

Parameterized complexity of a coupled-task scheduling problem

“…From this pioneer article on complexity, severals articles keep classifying in both modes (non cyclic and cyclic 3 ). For the non cyclic mode, we suggest the two following references [3] or [8] for more recent results. A recent result given by [15], in cycle mode, propose a efficient polynomialtime algorithm for the special case (a, L, b) (notice that in non cycle case the status of this problem is unknown).…”

Coupled Task Scheduling With Exact Delays: Literature Review and Models

“…The instances set includes a total number of 250 instances with 20 to 500 jobs, where the task processing times are in the range of 10 and 100, and the delay durations in the range of 300 and 1,300. Ahr et al (2004); Li and Zhao (2007); Brauner et al (2009);Blazewicz et al (2012) adopted a similar approach, i.e., taking values from a discrete uniform interval. The instances in Sherali and Smith (2005) consist of 8 to 14 jobs, with aj taken from the normal distribution with a mean of 30 time units and a standard deviation of 5 time units, i.e., N (30, 5).…”

“…To the best of our knowledge, Blazewicz et al (2012) provided the only review of research on coupled task scheduling. Their review includes (1) discussing known complexity results for the problem, (2) reviewing the state-of-the-art algorithms, and (3) evaluating the performance of algorithms over a set of instances with up to 838 tasks.…”