DMCA
A Note on Algebraic Hypercube Colorings
Cached
Download Links
- [wwwusers.di.uniroma1.it]
- [www.diag.uniroma1.it]
- DBLP
Other Repositories/Bibliography
BibTeX
@MISC{Finocchi_anote,
author = {Irene Finocchi and Emanuele G. Fusco and Rossella Petreschi},
title = {A Note on Algebraic Hypercube Colorings },
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
An L(1, 1)-coloring of the n-dimensional hypercube Qn assigns nodes of Qn which are at distance ≤ 2 with different colors. Such colorings find application, e.g., in frequency assignment in wireless networks and data distribution in parallel memory systems. Let χ 2 (Qn) be the minimum number of colors used in any L(1, 1)-coloring. Finding the exact value of χ 2 (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 χ 2 (Qn), independently of the choice of the group operation.
Keyphrases
algebraic hypercube coloring group theoretic flavour minimum number 2-approximate solution parallel memory system algebraic structure exact value n-dimensional hypercube qn efficient way coloring problem open problem current upper bound different color wireless network algebraic structure cannot data distribution group theory group operation frequency assignment
