TY - JOUR
AU - Pikies, Tytus
AU - Turowski, Krzysztof
AU - Kubale, Marek
PY - 2021/05/17
Y2 - 2022/01/21
TI - Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines
JF - Proceedings of the International Conference on Automated Planning and Scheduling
JA - ICAPS
VL - 31
IS - 1
SE - Main Track
DO -
UR - https://ojs.aaai.org/index.php/ICAPS/article/view/15970
SP - 262-270
AB - In this paper we consider a problem of job scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine.We provide several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality: Cmax (makespan) and ∑Cj (total completion time). We consider a variety of machine types in our paper: identical, uniform, and unrelated. Our results consist of delimitation of the easy (polynomial) and NP-hard problems within these constraints. We also provide algorithms, either polynomial exact algorithms for the easier problems, or algorithms with a guaranteed constant worst-case approximation ratio.In particular, we fill the gap on research for the problem of finding a schedule with the smallest ∑Cj on uniform machines. We address this problem by developing a linear programming relaxation technique with an appropriate rounding, which to our knowledge is a novelty for this criterion in the considered setting.
ER -