Jian Ni
ABSTRACT
In this paper, we study distributed channel assignment in wireless networks with applications to peer discovery in ad hoc wireless networks. We model channel assignment as a coloring problem for spatial point processes in which n nodes are located in a unit cube uniformly at random and each node is assigned one of K colors, where each color represents a channel. The objective is to maximize the spatial separation between nodes of the same color. In general, it is hard to derive the optimal coloring algorithm and therefore, we consider a natural greedy coloring algorithm, first proposed in [5]. We prove two key results: (i) with just a small number of colors when K is roughly of the order of log(n) loglog(n), the distance separation achieved by the greedy coloring algorithm asymptotically matches the optimal distance separation that can be achieved by an algorithm which is allowed to select the locations of the nodes but is allowed to use only one color, and (ii) when K = Omega(log(n)), the greedy coloring algorithm asymptotically achieves the best distance separation that can be achieved by an algorithm which is allowed to both optimally color and place nodes. The greedy coloring algorithm is also shown to dramatically outperform a simple random coloring algorithm. Moreover, the results continue to hold under node mobilities.
- D. Angelosante, E. Biglieri, and M. Lops. Neighbor discovery in wireless networks: A multiuser-detection approach. http://arxiv.org/abs/0704.3241, 2007.Google Scholar
- F. Baccelli and B. Blaszczyszyn. Stochastic Geometry and Wireless Networks Volume I: Theory. Foundations and Trends in Networking, NOW Publishers, 2009. Google ScholarDigital Library
- S. A. Borbash, A. Ephremides, and M. J. McGlynn. An asynchronous neighbor discovery algorithm for wireless sensor networks. Ad Hoc Networks, 5(7):998--1016, 2007. Google ScholarDigital Library
- R. J. Fowler, M. Paterson, and S. L. Tanimoto. Optimal packing and covering in the plane are NP-complete. Inf. Process. Lett., 12(3):133--137, 1981.Google ScholarCross Ref
- B.-J. Ko and D. Rubenstein. Distributed self-stabilizing placement of replicated resources in emerging networks. IEEE/ACM Transactions on Networking, 13(3):476--487, 2005. Google ScholarDigital Library
- D. D. Lin and T. J. Lim. Subspace-based active user identification for a collision-free slotted ad hoc network. IEEE Transactions on Communications, 52(4):612--621, 2004.Google ScholarCross Ref
- J. Luo and D. Guo. Neighbor discovery in wireless ad hoc networks based on group testing. In Proceedings of Allerton Conference on Communication, Control, and Computing, September 2008.Google Scholar
- C. McDiarmid. Random channel assignment in the plane. Random Structures and Algorithms, 22(2):187--212, 2003. Google ScholarDigital Library
- M. J. McGlynn and S. A. Borbash. Birthday protocols for low energy deployment and flexible neighbor discovery in ad hoc wireless networks. In MobiHoc, pages 137--145, 2001. Google ScholarDigital Library
- M. Mitzenmacher and E. Upfal. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, 2005. Google ScholarDigital Library
- M. D. Mitzenmacher. The power of two choices in randomized load balancing. IEEE Transactions on Parallel and Distributed Systems, 12(10):1094--1104, 2001. Google ScholarDigital Library
- J. Ni, R. Srikant, and X. Wu. Coloring spatial point processes with applications to peer discovery in large wireless networks, March 2010. Technical Report.Google Scholar
- M. Raab and A. Steger. "Balls into bins" -- a simple and tight analysis. In RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science, pages 159--170, 1998. Google ScholarDigital Library
- T. Richardson, R. Laroia, J. Li, A. Jovicic, and X. Wu. Methods and apparatus related to peer discovery and/or paging in peer to peer wireless communications, 2009. US Patent Application, publication No. WO/2009/009313.Google Scholar
- S. M. Ross. Stochastic Processes. John Wiley & Sons, 1996.Google Scholar
- D. Stoyan, W. S. Kendall, and J. Mecke. Stochastic Geometry and Its Applications. John Wiley & Sons, 1995.Google Scholar
- D. Tse and P. Viswanath. Fundamentals of Wireless Communication. Cambridge University Press, 2005. Google ScholarDigital Library
- S. Vasudevan, J. F. Kurose, and D. F. Towsley. On neighbor discovery in wireless networks with directional antennas. In INFOCOM, 2005.Google ScholarCross Ref
- L. Ying, R. Srikant, and G. Dullerud. Function computation in wireless sensor networks. Networked Sensing Information and Control, pages 93--114, 2008.Google ScholarCross Ref
Index Terms
- Coloring spatial point processes with applications to peer discovery in large wireless networks
Recommendations
Coloring spatial point processes with applications to peer discovery in large wireless networks
In this paper, we study distributed channel assignment in wireless networks with applications to peer discovery in ad hoc wireless networks. We model channel assignment as a coloring problem for spatial point processes in which n nodes are located in a ...
Coloring spatial point processes with applications to peer discovery in large wireless networks
Performance evaluation reviewIn this paper, we study distributed channel assignment in wireless networks with applications to peer discovery in ad hoc wireless networks. We model channel assignment as a coloring problem for spatial point processes in which n nodes are located in a ...
Performance evaluation of routing protocols for ad hoc wireless networks
A mobile ad hoc network is a collection of autonomous mobile nodes that communicate with each other over wireless links. Such networks are expected to play an increasingly important role in future civilian and military settings, being useful for ...
Comments