Channel assignment with separation in the Cartesian product of two cycles

The L(2,1)-coloring is an abstraction of assigning integer frequencies to radio transmitters such that transmitters that are one unit of distance apart receive frequencies that differ by at least two, and transmitters that are two units apart receive frequencies that differ by at least one. In particular, the L(2,1)-coloring in the two dimensional torus (the Cartesian product of two cycles) is considered. We describe approximation and exact algorithms to search L(2,1) colorings in the torus. The exact values on the L(2,1)-coloring of three infinite families of graphs: C/sub n//spl square/C/sub 5/, C/sub n//spl square/C/sub 6/ and C/sub n//spl square/C/sub 7/ are presented.