Backbone colouring and algorithms for TDMA scheduling

• Published in: Discrete Mathematics and Theoretical Computer Science Vol. 21; no. 3; pp. COV3 - 21
• Main Authors: Bensmail, Julien, Blanc, Thibaut, Cohen, Nathann, Havet, Frederic, Rocha, Leonardo
• Format: Journal Article
• Language: English
• Published: Nancy DMTCS 01.07.2019; Discrete Mathematics & Theoretical Computer Science
• Subjects: [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]; Access control; algorithmic complexity; Algorithms; backbone colouring; Computer Science; Discrete Mathematics; Graph coloring; Graph theory; Mathematical research; Optimization; Radio networks; Schedules; Scheduling; Scheduling (Management); Sensors; tdma scheduling; Time Division Multiple Access; Topology; Wireless communications; Wireless networks; France; Algorithmic complexity; Wireless networks; Backbone colouring; TDMA scheduling
• ISSN: 1462-7264; 1365-8050
• DOI: 10.23638/dmtcs-21-3-24

We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the BPRN-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the BMRN-colouring model, which can be used to model link scheduling problems where particular types of collisions must be avoided during the node transmissions. In this paper, we initiate the study of the BMRN-colouring model by providing several bounds on the minimum number of colours needed to BMRN-colour digraphs, as well as several complexity results establishing the hardness of finding optimal colourings. We also give a special focus on these considerations for planar digraph topologies, for which we provide refined results. Some of these results extend to the BPRN-colouring model as well. Keywords: Wireless networks, TDMA scheduling, Backbone colouring, Algorithmic complexity.