Abstract
In the Code Division Multiple Access (CDMA) framework, collisions that can occur in wireless networks are eliminated by assigning orthogonal codes to stations, a problem equivalent to that of coloring graphs associated to the physical network. In this paper we present new upper and lower bounds for two versions of the problem (hidden and primary collision avoidance – HP‐CA – or hidden collision avoidance only – H‐CA). In particular, optimal assignments for special topologies and heuristics for general topologies are proposed. The schemes show better average results with respect to existing alternatives. Furthermore, the gaps between the upper bound given by the heuristic solution, the lower bound obtained from the maximum‐clique problem, and the optimal solution obtained by branch and bound are investigated in the different settings. A scaling law is then proposed to explain the relations between the number of codes needed in Euclidean networks with different station densities and connection distances. The substantial difference between the two versions HP‐CA and H‐CA of the problem is investigated by studying the probabilistic distribution of connections as a function of the distance, and the asymptotic size of the maximum cliques.
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References
N. Abrahmson, The ALOHA system-Another alternative for computer communications, in: Proc. of FJCC(1970) pp. 281-285.
R. Battiti and M. Protasi, Reactive local search for the maximum clique problem, Technical Report TR-95-052, ICSI, Berkeley, CA (1995).
M. Bellare, O. Goldreich and M. Sudan, Free bits, PCPs and nonapproximability. Toward tight results, in: Proc. 36th Ann. Symp. on Foundations of Computer Science(IEEE Computer Society, Los Alamitos, CA, 1995) pp. 422-431.
A.A. Bertossi and M.A. Bonuccelli, Code assignment for hidden terminal interference avoidance in multihop packet radio networks, IEEE Transactions on Networking 3(4) (1995) 441-449.
D. Br´elaz, New methods to color the vertices of a graph, Communications of the ACM 22 (1979) 251-256.
I. Chlamtac and S. Kutten, On broadcasting in radio networks-Problem analysis and protocol design, IEEE Transactions on Communications (December 1985).
I. Chlamtac and S. Kutten, A spatial reuse TDMA/FDMA for mobile multi-hop radio networks, in: Proc. of IEEE INFOCOM(March 1985).
I. Chlamtac and S.S. Pinter, Distributed nodes organization algorithm for channel access in a multihop dynamic radio network, IEEE Transactions on Computers 36 (1987) 728-737.
I. Cidon and M. Sidi, Distributed assignment algorithms for multihop packet radio networks, IEEE Transactions on Computers 38 (1989) 1353-1361.
D. Johnson and M. Trick <nt>(eds.)</nt>, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, in press.
L. Hu, Distributed code assignments for CDMA packet radio networks, IEEE Transactions on Networking 1(6) (1993) 668-677.
S.M. Korman, The graph-coloring problem, in: Combinatorial Optimization, <nt>eds</nt>. N. Christophides, P. Toth and C. Sandi (Wiley, New York, 1979) pp. 211-235.
M. Kubale and B. Jackowski, A generalized implicit enumeration algorithm for graph coloring, Communications of the ACM 28 (1985) 412-418.
T. Makansi, Transmitted-oriented code assignment for multihop packet radio, IEEE Transactions on Communications 35 (1987) 1379-1382.
A. Mehrotra and M.A. Trick, A column generation approach to graph coloring, Technical report series, Graduate School of Industrial Administration, Carnegie Mellon University (1995).
R. Nelson and L. Kleinrock, Spatial TDMA: a collision-free multihop channel access protocol, IEEE Transactions on Communications 33 (1985) 934-944.
M.J. Post, A.S. Kershenbaum and P.E. Sarachik, Scheduling multihop CDMA networks in the presence of secondary conflicts, Algorithmica 4 (1989) 365-394. ssRoberto Battiti received the Laurea degree in physics from the University of Trento, Italy, in 1985 and was awarded a Ph.D. in computation and neural systems by the California Institute of Technology (Caltech) in 1990. He has been a consultant in the area of parallel computing and pattern recognition and since 1991 he has been with the Department of Mathematics of the University of Trento, Italy. His main research interests are heuristic algorithms for combinatorial problems, in particular reactive algorithms for maximum-clique, satisfiability, colorR Battiti et al. / Assigning codes in wireless networks 209 ing, code assignment in wireless networks, and algorithms for massively parallel architectures that can be realized as special purpose VLSI circuits. R. Battiti is a member of the ACM and of the IEEE Computer Society. Alan A. Bertossi was born in London, England, on January 7, 1956. He received the Laurea degree in computer science from the University of Pisa, Italy, in 1979. Afterwards, he worked as a System Programmer and Designer. From 1983 through 1994 he was with the Department of Computer Science, University of Pisa, first as a Research Associate and later as an Associate Professor. Since 1995 he has been with the Department of Mathematics, University of Trento, as a Professor of Computer Science. His main research interests are the design and analysis of algorithms for combinatorial problems, as well as the computational aspects of parallel, VLSI, distributed, real-time, and fault-tolerant systems. Maurizio A. Bonuccelli is Professor of Computer Science at the Dipartimento di Informatica, University of Pisa, Italy. He has been associated with that department since 1976, with the only exception of the years from 1990 until 1994 when he was a Professor of Computer Science at the University of Rome "La Sapienza". During 1981 he took a sabbatical leave at IBM T.J.Watson Research Center, Yorktown Heights, NY, working in the computer communications group, and spent September 1993 at ICSI, Berkeley, CA, with the TENET group. He has been and is involved in the organizing, program and steering committee of several international workshops and conferences. He is International Conference Coordinator of ACM SigMobile. His field of interest is the design and management of communication, computer networks, and distributed parallel processing systems, with a special emphasis on algorithmic and complexity issues.
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Battiti, R., Bertossi, A.A. & Bonuccelli, M.A. Assigning codes in wireless networks: bounds and scaling properties. Wireless Networks 5, 195–209 (1999). https://doi.org/10.1023/A:1019146910724
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DOI: https://doi.org/10.1023/A:1019146910724