4/20/2023 0 Comments Unit disk graph chromatic boundKuhn, F.: Faster deterministic distributed coloring through recursive list coloring. Kuhn, F.: The price of locality: exploring the complexity of distributed coordination primitives. Hassinen, M., Kaasinen, J., Kranakis, E., Polishchuk, V., Suomela, J., Wiese, A.: Analysing local algorithms in location-aware quasi-unit-disk graphs. Halldórsson, M., Konrad, C.: Improved distributed algorithms for coloring interval graphs with application to multicoloring trees. Gräf, A., Stumpf, M., Weißenfels, G.: On coloring unit disk graphs. Ghaffari, M., Kuhn, F.: Deterministic distributed vertex coloring: simpler, faster, and without network decomposition. In: Proceedings of the ACM Symposium on Discrete Algorithms (2021) Ghaffari, M., Grunau, C., Rozhoň, V.: Improved deterministic network decomposition. Gerke, S., McDiarmid, C.J.H.: Graph imperfection. 355–370 (2015)Įsperet, L., Julliot, J., de Mesmay, A.: Distributed coloring and the local structure of unit-disk graphs. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA’15), pp. 86(1–3), 165–177 (1990)Įlkin, M., Pettie, S., Su, H.-H.: \((2\Delta -1)\)-edge-coloring is much easier than maximal matching in the distributed setting. In: Proceedings of the 3rd International Conference on Wireless Internet (WICON ’07), Article 6, pp. 24, 247–250 (1915)Ĭho, S.Y., Adjih, C., Jacquet, P.: Heuristics for network coding in wireless networks. 22(5–6), 363–379 (2010)īarenboim, L., Elkin, M., Pettie, S., Schneider, J.: The locality of distributed symmetry breaking. Keywordsīarenboim, L., Elkin, M.: Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition. We conjecture that every unit-disk graph G has average degree at most \(4\omega (G)\), which would imply the existence of a \(O(\log n)\) round algorithm coloring any unit-disk graph G with (approximatively) \(4\omega (G)\) colors. This algorithm is based on a study of the local structure of unit-disk graphs, which is of independent interest. Moreover, when \(\omega (G)=O(1)\), the algorithm runs in \(O(\log ^* n)\) rounds. When nodes do not know their coordinates in the plane, we give a distributed algorithm in the LOCAL model that colors every unit-disk graph G with at most \(5.68\omega (G)\) colors in \(O(\log ^3 \log n)\) rounds. This improves upon a classical 3-approximation algorithm for this problem, for all unit-disk graphs whose chromatic number significantly exceeds their clique number. In the location-aware setting (when nodes know their coordinates in the plane), we give a constant time distributed algorithm coloring any unit-disk graph G with at most \((3 \epsilon )\omega (G) 6\) colors, for any constant \(\epsilon >0\), where \(\omega (G)\) is the clique number of G. In this paper, we consider two natural distributed settings. In this context it is important to bound not only the complexity of the coloring algorithms, but also the number of colors used. Cela avait été conjecturé par Alon, Grytczuk, Haluszczak et Riordan en 2002.Coloring unit-disk graphs efficiently is an important problem in the global and distributed settings, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. Vendredi 6 mars 2020, Louis Esperet (G-SCOP, Grenoble) à 10h au LIPĪbstract: On montre que l'on peut colorier les graphes planaires avec un nombre constant de couleurs, de manière à ce que sur tout chemin de taille paire, la suite de couleurs sur la première motié du chemin diffère de la suite de couleurs sur la seconde moitié.Polynomial and sub-exponential time, up to an arbitrarily small constant in the Title: On Multicolour Ramsey Numbers and Subset-Colouring of Hypergraphsįor n >= s > r >= 1 and k >= 2, write n \erarrow (s)_$, hence we preciselyĬharacterize the approximability of the problem for the whole spectrum between Vendredi à 10h30, Lena Yuditsky (Université Libre de Bruxelles) Vendredi 23 Septembre 2022, Alexandre Wesolek (Simon Fraser) Ils sont parfois remplacés par des séminaires GRAA (Graphes en Rhone Alpes Auvergne) communs au laboratoire LIP / LIRIS / LIMOS et G-SCOP.Įn espérant vous voir nombreux pour des séminaires en présentiel ou en distanciel. Vu la situation sanitaire actuelle, les séminaires n'ont pas lieu à une fréquence régulière. Si vous désirez parler au séminaire, merci de contacter Nicolas Bousquet ou Rémi Watrigant voir les anciennes présentations, vous pouvez consulter la page d' archives. Rassemble les chercheurs de la région lyonnaise intéressés par les graphes, en particulier les chercheurs des équipes MC2 du LIP et Goal du LIRIS.
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