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Channel Assignment with Separation for Interference Avoidance in Wireless Networks
March 2003 (vol. 14 no. 3)
pp. 222-235

Abstract—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}){\hbox{-}}\rm 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}){\hbox{-}}\rm 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{\hbox{-}}\rm 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.

[1] R. Battiti, A.A. Bertossi, and M.A. Bonuccelli, “Assigning Codes in Wireless Networks: Bounds and Scaling Properties,” Wireless Networks, vol. 5, pp. 195-209, 1999.
[2] A.A. Bertossi and M.A. Bonuccelli, “Code Assignment for Hidden Terminal Interference Avoidance in Multihop Packet Radio Networks,” IEEE/ACM Trans. Networking, vol. 3 pp. 441-449, 1995.
[3] A.A. Bertossi and M.C. Pinotti, “Mappings for Conflict-Free Access of Paths in Bidimensional Arrays, Circular Lists, and Complete Trees,” J. Parallel and Distributed Computing, vol. 62, pp. 1314-1333, 2002.
[4] A.A. Bertossi, M.C. Pinotti, and R. Tan, “Efficient Use of Radio Spectrum in Wireless Networks with Channel Separation between Close Stations,” DIAL M for Mobility; Int'l ACM Workshop Discrete Algorithms and Methods for Mobile Computing, 2000.
[5] H.L. Bodlaender, T. Kloks, R.B. Tan, and J. van Leeuwen, “Approximationλ-Coloring on Graphs,” Proc. Int'l Symp. Theoretical Aspects of Computer Science, 2000.
[6] G.J. Chang and D. Kuo, “The$\big. L(2,1){\hbox{-}}\rm Labeling\bigr.$Problem on Graphs,” SIAM J. Discrete Math., vol. 9, pp. 309-316, 1996.
[7] I. Chlamtac and S.S. Pinter, “Distributed Nodes Organizations Algorithm for Channel Access in a Multihop Dynamic Radio Network,” IEEE Trans. Computers, vol. 36, pp. 728-737, 1987.
[8] D. Goodman, J. Borras, N. Mandayam, and R. Yates, INFOSTATIONS: A New System Model for Data and Messaging Services Proc. IEEE Vehicular Technology Conf., vol. 2, pp. 969-973, 1997.
[9] H. Griffin, Elementary Theory of Numbers. New York: McGraw-Hill, 1954.
[10] J.R. Griggs and R.K. Yeh, “Labelling Graphs with a Condition at Distance$\big. 2\bigr.$,” SIAM J. Discrete Math., vol. 5, pp. 586-595, 1992.
[11] W.K. Hale, “Frequency Assignment: Theory and Application,” Proc. IEEE, vol. 68, pp. 1497-1514, 1980.
[12] I. Katzela and M. Naghshineh, “Channel Assignment Schemes for Cellular Mobile Telecommunication Systems: A Comprehensive Survey,” IEEE Personal Comm., vol. 3, no. 3, pp. 10-31, June 1996.
[13] T. Makansi, “Transmitted Oriented Code Assignment for Multihop Packet Radio,” IEEE Trans. Comm., vol. 35, pp. 1379-1382, 1987.
[14] S.T. McCormick, “Optimal Approximation of Sparse Hessians and Its Equivalence to a Graph Coloring Problem,” Math. Programming, vol. 26, pp. 153–171, 1983.
[15] D. Sakai, “Labeling Chordal Graphs: Distance Two Condition,” SIAM J. Discrete Math., vol. 7, pp. 133-140, 1994.
[16] A. Sen, T. Roxborough, and S. Medidi, “Upper and Lower Bounds of a Class of Channel Assignment Problems in Cellular Networks,” technical report, Arizona State Univ., 1997.
[17] D.H. Smith, S. Hurley, and S.U. Thiel, “Improving Heuristics for the Frequency Assignment Problem,” European J. Operation Research, vol. 107, pp. 76-86, 1998.
[18] A. Tanenbaum, Computer Networks. Prentice Hall, 1988.
[19] J. Van den Heuvel, R.A. Leese, and M.A. Shepherd, “Graph Labelling and Radio Channel Assignment,” J. Graph Theory, vol. 29, pp. 263-283, 1998.
[20] J. Zander, “Trends and Challenges in Resource Management Future Wireless Networks,” Proc. IEEE Wireless Comm. and Networks Conf., 2000.

Index Terms:
Wireless networks, channel assignment, interferences, rings, cellular grids, bidimensional grids, L(2,1,1){\hbox{-}}\rm coloring , L(\delta_1,1,\ldots,1){\hbox{-}}\rm coloring .
Citation:
Alan A. Bertossi, Cristina M. Pinotti, Richard B. Tan, "Channel Assignment with Separation for Interference Avoidance in Wireless Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 3, pp. 222-235, March 2003, doi:10.1109/TPDS.2003.1189581
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