Distributed coverage verification in sensor networks without location information

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2008, Pages 4170-4176

  Tahbaz Salehi, Alireza ^a   Jadbabaie, Ali ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

OPTIMIZATION; SENSOR NETWORKS;

COMPUTATIONAL HOMOLOGY; COVERAGE HOLES; HIGHER DIMENSIONS; LOCATION INFORMATION; OPTIMIZATION PROBLEMS; PROXIMITY GRAPHS; SIMPLICIAL COMPLEX; SUB-GRADIENT METHODS;

COMPLEX NETWORKS;

EID: 51849103844     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2008.4738751     Document Type: Conference Paper

References (25)

1. D. Gage, "Command control for many-robot systems," Unmanned Systems Magazine, vol. 10, no. 4, pp. 28-34, 1992.
2. S. Meguerdichian, F. Koushanfar, M. Potkonjak, and M. Srivastava, "Coverage problems in wireless ad-hoc sensor network," in IEEE INFOCOM, 2001, pp. 1380-1387.
3. A. Ganguli, J. Cortes, and F. Bullo, "Distributed deployment of asynchronous guards in art galleries," in Proceedings of American Control Conference, Minneapolis, MN, June 2006, pp. 1416-1421.
4. R. Ghrist and A. Muhammad, "Coverage and hole-detection in sensor networks via homology," in Proceedings of the Fourth Inernational Symposium on Information Processing in Sensor Networks, Los Angeles, CA, April 2005, pp. 254-260.
5. V. de Silva, R. Ghrist, and A. Muhammad, "Blind swarms for coverage in 2-D," in Robotics: Science and Systems, Cambridge, MA, June 2005.
6. V. de Silva and R. Ghrist, "Coordinate-free coverage in sensor networks with controlled boundaries via homology," The International Journal of Robotics Research, vol. 25, no. 12, pp. 1205-1222, 2006.
7. -, "Coverage in sensor networks via persistent homology," Algebraic and Geometric Topology, pp. 339-358, 2007.
8. A. Muhammad and M. Egerstedt, "Control using higher order Laplacians in network topologies," in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, 2006, pp. 1024-1038.
9. A. Muhammad and A. Jadbabaie, "Decentralized computation of homology groups in networks by gossip," in Proceedings of American Control Conference, New York, NY, 2007, pp. 3438-3443.
10. N. Z. Shor, K. C. Kiwiel, and A. Ruszcayǹski, Minimization Methods for Non-Differentiable Functions. New York, NY: Springer-Verlag New York, Inc., 1985.
11. R. Olfati-Saber and R. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520-1533, Sept. 2004.
12. S. Cabello and B. Mohar, "Finding shortest non-separating and noncontractible cycles for topologically embedded graphs," Discrete and Computational Geometry, vol. 37, no. 2, pp. 213-235, 2007.
13. S. Cabello, M. DeVos, J. Erickson, and B. Mohar, "Finding one tight cycle," submitted to 19th Annual ACM-SIAM Symposium on Discrete Algorithms (2008).
14. Éric Colin de Verdière and F. Lazarus, "Tightening non-simple paths and cycles on surfaces," in ACM-SIAM Symposium on Discrete Algorithms, Jan. 2006, pp. 192-201.
15. -, "Optimal system of loops on an orientable surface," Discrete and Computational Geometry, vol. 33, no. 3, 2005.
16. E. W. Chambers, J. Erickson, and P. Worah, "Testing contractibility in planar Rips complexes," submitted to 19th Annual ACM-SIAM Symposium on Discrete Algorithms (2008).
17. E. W. Chambers, V. de Silva, J. Erickson, and R. Ghrist, "Rips complexes of planar point sets," under Preperation. [Online]. Available: http://www.cs.uiuc.edu/~jeffe/pubs/rips.html
18. A. Hatcher, Algebraic Topology. Cambridge University Press, 2002.
19. B. Eckmann, "Harmonische Funktionen und Randwertaufgaben Einem Komplex," Commentarii Math. Helvetici, vol. 17, pp. 240-245, 1945.
20. A. M. Duval and V. Reiner, "Shifted simplicial complexes are Laplacian integral," Transactions of the American Mathematical Society, vol. 354, no. 11, pp. 4313-4344, 2002.
21. L. Vietoris, "Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen," Mathematische Annalen, vol. 97, no. 1, pp. 454-472, 1927.
22. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Gossip algorithms: Design, analysis and applications," in IEEE Infocom, vol. 3, March 2005, pp. 1653-1664.
23. C. Chen and D. Freedman, "Quantifying homology classes II: Localization and stability," 2007, Preprint. [Online]. Available: arXiv:0709.2512v2
24. D. L. Donoho and J. Tanner, "Sparse nonnegative solution of underdetermined linear equations by linear programming," Proceedings of the National Academy of Sciences, vol. 102, no. 27, pp. 9446-9451, 2005.
25. S. Boyd, L. Xiao, and A. Mutapcic, "Subgradient methods," Oct. 2003, Lecture notes. [Online]. Available: http://www.stanford.edu/class/ee392o/ subgrad-method.pdf