@ARTICLE{Pikies_T._Better_2019, author={Pikies, T. and Kubale, M.}, volume={67}, number={No. 1}, journal={Bulletin of the Polish Academy of Sciences Technical Sciences}, pages={31-36}, howpublished={online}, year={2019}, abstract={The goal of this paper is to explore and to provide tools for the investigation of the problems of unit-length scheduling of incompatible jobs on uniform machines. We present two new algorithms that are a significant improvement over the known algorithms. The first one is Algorithm 2 which is 2-approximate for the problem Qm|pj  = 1, G = bisubquartic|Cmax. The second one is Algorithm 3 which is 4-approximate for the problem Qm|pj  = 1, G = bisubquartic|ΣCj, where m ∈ \{2, 3, 4\}. The theory behind the proposed algorithms is based on the properties of 2-coloring with maximal coloring width, and on the properties of ideal machine, an abstract machine that we introduce in this paper.}, type={Artykuły / Articles}, title={Better polynomial algorithms for scheduling unit-length jobswith bipartite incompatibility graphs on uniform machines}, URL={http://www.czasopisma.pan.pl/Content/111100/PDF/03_031-036_00776_Bpast.No.67-1_06.02.20.pdf}, doi={10.24425/bpas.2019.127335}, keywords={approximation algorithm, graph coloring, incompatible job, polynomial algorithm, scheduling, uniform machine, unit-time job}, }