# Channel Assignment with Separation for Interference Avoidance in Wireless Networks

Bertossi, Alan and Pinotti, Cristina M. and Tan, Richard (2002) Channel Assignment with Separation for Interference Avoidance in Wireless Networks. UNSPECIFIED. (In Press)

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Given an integer $\sigma > 1$, a vector $(\delta_1, \delta_2, \ldots, \delta_{\sigma-1})$ of nonnegative integers, and an undirected graph $G=(V,E)$, an $L(\delta_1, \delta_2, \ldots,\delta_{\sigma-1})$-coloring of $G$ is a function $f$ from the vertex set $V$ to a set of nonnegative integers such that $| f(u) -f(v) | \ge \delta_i$, if $d(u,v) = i, \ 1 \le i \le \sigma-1, \$ where $d(u,v)$ is the distance (i.e. the minimum number of edges) between the vertices $u$ and $v$. An optimal $L(\delta_1, \delta_2, \ldots,\delta_{\sigma-1})$-coloring for $G$ is one using the smallest range $\lambda$ of integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e. colors) assigned to interfering stations (i.e. vertices) at distance $i$ must be at least $\delta_i$ apart, while the same channel can be reused in vertices whose distance is at least $\sigma$. In particular, two versions of the coloring problem -- $L(2,1,1)$, and $L(\delta_1, 1, \ldots,1)$ -- are considered. Since these versions of the problem are $NP$-hard for general graphs, efficient algorithms for finding optimal colorings are provided for specific graphs modeling realistic wireless networks including rings, bidimensional grids, and cellular grids.
Item Type: Departmental Technical Report Information Engineering and Computer Science Q Science > QA Mathematics > QA075 Electronic computers. Computer science Wireless Networks, Channel Assignment, Interferences, Rings, Cellular Grids, Bidimensional Grids, $L(2,1,1)$-coloring, $L(\delta_1,1,\ldots,1)$-coloring Accepted in september 2002 for publication on IEEE Transaction on Parallel and Distributed Systems DIT-02-078 12 Dec 2002