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• W2152173972 abstract "An L(1, 1)-coloring of the n-dimensional hypercube Qn assigns nodes of Qn which are at distance les 2 with different colors. Such colorings find application, e.g., in frequency assignment in wireless networks and data distribution in parallel memory systems. Let chi2 macr(Qn) be the minimum number of colors used in any L(1, 1)-coloring. Finding the exact value of chi2 macr(Qn) is still an open problem, and only 2-approximate solutions are currently known. In this paper we expose some connections between group theory and the L(1, 1)-coloring problem. Namely, we unfold the algebraic structure on which the best available L(1, 1)-coloring algorithms of Qn are based, thus giving a group theoretic flavour to existing L(1, 1)-colorings. We show that identifying groups such that the inverse of each element is the element itself yields a simple and efficient way to obtain L(1, 1)-colorings of the hypercube. We also prove that such colorings are balanced and that every coloring algorithm based on this algebraic structure cannot improve the current upper bound on chi2 macr(Qn), independently of the choice of the group operation." @default.
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• W2152173972 date "2008-04-01" @default.
• W2152173972 modified "2023-09-27" @default.
• W2152173972 title "A Note on Algebraic Hypercube Colorings" @default.
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• W2152173972 doi "https://doi.org/10.1109/itng.2008.173" @default.
• W2152173972 hasPublicationYear "2008" @default.
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