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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Finocchi, I. Fusco, E.G. Petreschi, R. |
| Copyright Year | 2008 |
| Description | Author affiliation: Univ. di Roma La Sapienza, Rome (Finocchi, I.; Fusco, E.G.; Petreschi, R.) |
| Abstract | An L(1, 1)-coloring of the n-dimensional hypercube $Q_{n}$ assigns nodes of $Q_{n}$ 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 $chi_{2}$ $macr(Q_{n})$ be the minimum number of colors used in any L(1, 1)-coloring. Finding the exact value of $chi_{2}$ $macr(Q_{n})$ 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 $Q_{n}$ 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 $chi_{2}$ $macr(Q_{n}),$ independently of the choice of the group operation. |
| Starting Page | 869 |
| Ending Page | 874 |
| File Size | 475585 |
| Page Count | 6 |
| File Format | |
| ISBN | 0769530990 |
| DOI | 10.1109/ITNG.2008.173 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2008-04-07 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Upper bound Wireless networks Binary codes Hypercubes Frequency Polynomials Remuneration Information technology Interference constraints |
| Content Type | Text |
| Resource Type | Article |
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