Channel assignment with separation in the Cartesian product of two cycles

A. Vesel1
1Department of Mathematics, University of Maribor, Maribor, Slovenia

Tóm tắt

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.

Từ khóa

#Radio transmitters #Wireless networks #Heuristic algorithms #Radio frequency #Interference #Hypercubes #Mathematics #Approximation algorithms #Computer networks #Receivers

Tài liệu tham khảo

weiss, 1995, Data Structures and Algorithm Analysis klavzar, 2001, Computing Graph Invariants on Rotagraphs Using Dynamic Algorithm Approach The Case of (2 1)-colorings and Independence Numbers, 779, 1 10.1016/0012-365X(89)90214-8 10.1109/81.917988 jha, 2000, On l(2,l)-labeling of the cartesian product of a cycle and a path, Ars Combinatoria, 81 10.1007/3-540-46784-X_33 10.1137/S0895480193245339 10.1109/TPDS.2003.1189581 10.1109/81.886984 10.1016/0012-365X(93)E0098-O 10.1137/S0895480199351859 10.1002/(SICI)1097-0118(199605)22:1<47::AID-JGT7>3.3.CO;2-D georges, 1995, Generalized vertex labelings with a condition at distance two, Congressus Numerantium, 109, 141 10.1002/(SICI)1097-0118(199812)29:4<263::AID-JGT5>3.0.CO;2-V 10.1137/0405048