Distributed averaging via lifted Markov chains

IEEE Transactions on Information Theory

Volumn 56, Issue 1, 2010, Pages 634-647

  Jung, Kyomin ^a   Shah, Devavrat ^a,b   Shin, Jinwoo ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b USA   (United States)

Author keywords

Consensus; Lifting; Linear averaging; Markov chain; Nonreversible; Pseudo lifting; Random walk

Indexed keywords

CONVERGENCE TIME; DISTRIBUTED CONTROL; DISTRIBUTED OPTIMIZATION; DOUBLING DIMENSIONS; ITERATIVE ALGORITHM; LINEAR AVERAGING; LINEAR ESTIMATION; MARKOV CHAIN; METROPOLIS-HASTINGS METHOD; MIXING TIME; NETWORK GRAPH; RANDOM WALK; RATE OF CONVERGENCE; TOPOLOGICAL CONSTRAINTS;

ALGORITHMS; APPROXIMATION THEORY; COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; TOPOLOGY;

MARKOV PROCESSES;

EID: 73849146043     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2034777     Document Type: Article

References (32)

1. D. J. Aldous, "Some inequalities for reversible Markov chains," J. London Math. Soc., vol. 25, pp. 564-576, 1982.
2. n, " Bull. Soc. Math. France, vol. 111, no. 4, pp. 429-448, 1983.
3. V. D. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis, "Convergence in multiagent coordination, consensus, and flocking," in Proc. Joint 44th IEEE Conf. Decision and Control and European Control Conference (CDC-ECC'05), Seville, Sapin, Dec. 2005, pp. 2996-3000.
4. S. Boyd, P. Diaconis, J. Sun, and L. Xiao, "Fastest mixing Markov chain on a path," Amer. Math. Monthly, vol. 113, no. 1, pp. 70-74, 2006.
5. S. Boyd, P. Diaconis, and L. Xiao, "Fastest mixing Markov chain on a graph," SIAM Rev., vol. 46, no. 4, pp. 667-689, 2004.
6. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Gossip algorithms: Design, analysis and applications," in Proc. IEEE INFOCOM 2005, Niami, FL, 2005, pp. 1653-1664.
7. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Randomized gossip algorithms," IEEE/ACM Trans. Netw., vol. 14, pp. 2508-2530, 2006.
8. F. Chen, L. Lovász, and I. Pak, "Lifting Markov chains to speed up mixing," in Proce. 36th Annu. ACM Symp. Theory of Computing (STOC'99), New York, 1999, pp. 275-281, published by ACM Press.
9. S. Dasgupta and Y. Freund, "Random projection trees and low dimensional manifolds," in Proc. 40th Annu. ACM Symp. Theory of Computing (STOC'08), New York, 2008, pp. 537-546, published by ACM Press.
10. P. Diaconis, S. Holmes, and R. Neal, "Analysis of a non-reversible Markov chain sampler," Ann. Appl. Probab., vol. 10, pp. 726-752, 2000.
11. A. G. Dimakis, A. D. Sarwate, and M. J. Wainwright, "Geographic gossip: Efficient aggregation for sensor networks," in Proc. 5th Int. ACM/IEEE Symp. Information Processing in Sensor Networks (IPSN'06), Nashville, TN, Apr. 2006, pp. 69-76.
12. A. Gupta, R. Krauthgamer, and J. R. Lee, "Bounded geometries, fractals, and low-distortion embeddings," in Proc. 44th Annu. IEEE Symp. Foundations of Computer Science (FOCS'03), Washington, DC, 2003, p. 534, published by the IEEE Computer Society.
13. W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications," Biometrika, vol. 57, pp. 97-109, 1970.
14. J. Heinonen, Ed., Lectures on Analysis on Metric Spaces.. Berlin, Germany: Springer, 2001.
15. R. Horn and C. Johnson, Eds., Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press., 1985.
16. A. Jadbabaie, J. Lin, and A. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Aut. Control, vol. 48, no. 6, pp. 988-1001, 2003.
17. D. Kempe, A. Dobra, and J. Gehrke, "Gossip-based computation of aggregate information," in Proc. 44th Annu. IEEE Symp. Foundations of Computer Science (FOCS'03), Washington, DC, 2003, p. 482, published by the IEEE Computer Society.
18. D. Kempe and F. McSherry, "A decentralized algorithm for spectral analysis," in Proc. 36th Annu. ACM Symp. Theory of Computing (STOC'04), New York, 2004, pp. 561-568, published by ACM Press.
19. C. Kenyon, E. Mossel, and Y. Peres, "Glauber dynamics on trees and hyperbolic graphs," in Proc. IEEE Symp. Foundations of Computer Science, Las Vegas, NV, 2001, pp. 568-578.
20. P. Kolman and C. Scheideler, "Improved bounds for the unsplittable flow problem," in Proc. 13th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA'02), Philadelphia, PA, 2002, pp. 184-193, published by SIAM.
21. M. Koubarakis, C. Tryfonopoulos, S. Idreos, and Y. Drougas, "Selective information dissemination in p2p networks: Problems and solutions," SIGMOD Rec., vol. 32, no. 3, pp. 71-76, 2003.
22. T. Leighton and S. Rao, "Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms," in Proc. 29th Annu. Symp. Foundations of Computer Science (FOCS'88), White Plains, NY, 1988, pp. 422-431.
23. L. Lovasz and P. Winkler, D. Aldous and J. Propp, Eds., "Mixing times," Microsurveys in Discrete Probability, ser. DIMACS Series in Discrete Mathematics and Theory of Computer Science, pp. 85-133, 1998.
24. S. Madden, M. J. Franklin, J. M. Hellerstein, and W. Hong, "Tag: A tiny aggregation service for ad-hoc sensor networks," SIGOPS Oper. Syst. Rev., vol. 36, no. SI, pp. 131-146, 2002.
25. D. M. Malioutov, J. K. Johnson, and A. S. Willsky, "Walk-sums and belief propagation in gaussian graphical models," J. Mach. Learn. Res., vol. 7, pp. 2031-2064, 2006.
26. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys., vol. 21, pp. 1087-1092, 1953.
27. D. Mosk-Aoyama and D. Shah, "Fast distributed algorithms for computing separable functions," IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 2997-3007, Jul. 2008.
28. A. Nedic and A. Ozdaglar, "Distributed subgradient methods for multiagent optimization," IEEE Trans. Autom. Control, LIDS report 2755, to be published.
29. P. Diaconis and L. Saloff-Coste, "Moderate growth and random walk on finite groups," Geometric and Functional Analysis, vol. 4, no. 1, pp. 1-36, 1994.
30. K. Savla, F. Bullo, and E. Frazzoli, "On traveling salesperson problems for Dubins' vehicle: Stochastic and dynamic environments," in Proc. IEEE Conf. Decision and Control and european Control Conf. (CDC-ECC), Seville, Spain, Dec. 2005, pp. 4530-4535.
31. J. Tsitsiklis, "Problems in Decentralized Decision Making and Computation," Ph.D. dissertation, Lab. Information and Decision Systems, MIT, Cambridge, MA, 1984.
32. L. Xiao and S. Boyd, "Fast linear iterations for distributed averaging," Syst. Contr. Lett., vol. 53, pp. 65-78, 2004.