Topology for distributed inference on graphs

IEEE Transactions on Signal Processing

Volumn 56, Issue 6, 2008, Pages 2609-2613

  Kar, Soummya ^a   Aldosari, Saeed ^b   Moura, José M F ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Algebraic connectivity; Cayley; Consensus algorithm; Distributed detection; Laplacian; Ramanujan; Random graphs; Sensor networks; Small world; Spectral graph theory; Topology optimization

Indexed keywords

ALGEBRA; DECISION MAKING; LAPLACE EQUATION; PARALLEL ALGORITHMS; SENSOR NETWORKS; SHAPE OPTIMIZATION;

ALGEBRAIC CONNECTIVITY; RAMANUJAN GRAPHS; RANDOM GRAPHS; SPECTRAL GRAPH THEORY;

GRAPH THEORY;

EID: 44849127203     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.923536     Document Type: Article

References (23)

1. B. Bollobás, Modern Graph Theory. New York: Springer Verlag, 1998.
2. R. Olfati-Saber and R.M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Autom. Control, vol. 49, no. 9, p. 1520-1533, Sep. 2004.
3. J. N. Tsitsiklis, "Problems in decentralized decision making and computation," Ph.D. dissertation, Massachusetts Inst. of Technology, Cambridge, MA, 1984.
4. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Autom. Control, vol. AC-48, no. 6, pp. 988-1001, Jun. 2003.
5. L. Xiao and S. Boyd, "Fast linear iterations for distributed averaging," Syst. Control Lett., vol. 53, pp. 65-78, 2004.
6. R. Olfati-Saber, "Ultrafast consensus in small-world networks," in Proc. 2005 Amer. Control Conf., Jun. 2005, vol. 4, pp. 2371-2378.
7. S. A. Aldosari and J. M. F. Moura, "Distributed detection in sensor networks: Connectivity graph and small-world networks," in Proc. 39th Asilomar Conf. Signals, Systems, Computers, Pacific Grove, CA, Oct. 2005, pp. 230-234.
8. M. R. Murty, "Ramanujan graphs," J. Ramanujan Math. Soc., vol. 18, no. 1. pp. 1-20. 2003.
9. S. Kar, S. A. Aldosari, and J. M. F. Moura, "Topology for distributed inference on graphs,", Jun. 2006 [Online]. Available: http://www.arxiv.org/abs/cs/0606052, 30 pp.
10. L. Xiao and S. Boyd, "Fast linear iteration for distributed averaging," Syst. Control Lett., vol. 53, pp. 65-78, Sep. 2004.
11. F. R. K. Chung, Spectral Graph Theory. Providence, RI: Amer. Mathematical Soc., 1997.
12. S. Kar and J. M. F. Moura, "Ramanujan topologies for decision making in sensor networks," in Proc. 44th Allerton Conf. Communication, Control, Computing, Monticello, IL, Sep. 2006.
13. N. Alon, "Eigenvalues and expanders," Combinatorica, vol. 6, pp. 83-96, 1986.
14. A. Lubotzky, R. Phillips, and P. Sarnak, "Ramanujan graphs," Combinatorica, vol. 8, no. 3, pp. 261-277, 1988.
15. S. Camiz and S. Stetani, Matrices and Graphs: Theory and Applications Singapore: World Scientific, 1996.
16. G. Margulis, "Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators," J. Probl. Inf. Transm., vol. 24, no. 1, pp. 39-46, 1988.
17. M. Morgenstern, "Existence and explicit construction of q + 1 regular Ramanujan graphs for every prime power q" J. Comb. Theory, ser. B, vol. 62, pp. 44-62, 1994.
18. O. Reingold, S. P. Vadhan, and A. Wigderson, "Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors," in Proc. IEEE Symp. Foundations Computer Science, 2000, pp. 3-13.
19. A. Berger and J. Lafferty, "Probabilistic decoding of low-density Cayley codes," in Proc. Canadian Workshop on Information Theory, Toronto, ON, Canada, 1997.
20. D. J. Watts and S. H. Strogats, "Collective dynamics of small-world networks," Nature, vol. 393, pp. 440-442, 1998.
21. J. M. Kleinberg, "Navigation in a small world," Nature, vol. 406, p. 845, Aug. 2000.
22. A. E. Motter, C. Zhou, and J. Kurths, "Network synchronization, diffusion, and he paradox of heterogeneity," Phys. Rev. E, vol. 71, 2005.
23. N. C. Wormald, "Models ot random regular graphs," in Models of Random Regular Graphs, ser. Lecture Note Series. London, U.K.: London Mathematical Soc., 1999, vol. 267, pp. 239-298.