Reduction algorithm for simplicial complexes

Proceedings - IEEE INFOCOM

Volumn , Issue , 2013, Pages 475-479

  Vergne, A ^a   Decreusefond, L ^a   Martins, P ^a  

^a INSTITUT TELECOM   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC TOPOLOGY; COVERAGE PROBLEM; NASH EQUILIBRIA; REDUCTION ALGORITHMS; SIMPLICIAL COMPLEX; UPPER BOUND;

TOPOLOGY; WIRELESS SENSOR NETWORKS;

ALGORITHMS;

EID: 84883057233     PISSN: 0743166X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/INFCOM.2013.6566818     Document Type: Conference Paper

References (19)

1. X. Bai, S. Kumar, D. Xuan, Z. Yun, and T. H. Lai. Deploying wireless sensors to achieve both coverage and connectivity. In Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing, MobiHoc 06, pages 131-142, New York, NY, USA, 2006. ACM.
2. E. Campos-Nanez, A. Garcia, and C. Li. A game-theoretic approach to efficient power management in sensor networks. Oper. Res., 56(3):552-561, 2008.
3. V. de Silva and G. Carlsson. Topological estimation using witness complexes. IEEE Symposium on Point-based Graphic, pages 157-166, 2004.
4. V. de Silva and R. Ghrist. Coordinate-free coverage in sensor networks with controlled boundaries via homology. International Journal of Robotics Research, 25, december 2006.
5. L. Decreusefond and E. Ferraz. On the one dimensional Poisson random geometric graph. Journal of Probability and Statistics, 2011. Art. ID 350382, 21.
6. L. Decreusefond, E. Ferraz, H. Randriambololona, and A. Vergne. Simplicial homology of random configurations. http://hal-instituttelecom. archives-ouvertes.fr/hal-00578955, May 2012.
7. P. D?otko, R. Ghrist, M. Juda, and M. Mrozek. Distributed computation of coverage in sensor networks by homological methods. Applicable Algebra in Engineering, Communication and Computing, pages 1-30. 10.1007/s00200-012-0167-7.
8. Q. Fang, J. Gao, and L. Guibas. Locating and bypassing routing holes in sensor networks. In INFOCOM 2004. Twenty-third AnnualJoint Conference of the IEEE Computer and Communications Societies, volume 4, pages 2458-2468 vol.4, march 2004.
9. R. Ghrist and A. Muhammad. Coverage and hole-detection in sensor networks via homology. In Proceedings of the 4th international symposium on Information processing in sensor networks, IPSN 05, Piscataway, NJ, USA, 2005. IEEE Press.
10. A. Hatcher. Algebraic Topology. Cambridge University Press, 2002.
11. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater. Fundamentals of domination in graphs, volume 208 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York, 1998.
12. T. Kaczynski, M. Mrozek, and M. Slusarek. Homology computation by reduction of chain complexes. Comput. Math. Appl., 35(4):59-70, 1998.
13. M. Kahle. Random geometric complexes. Discrete & Computational Geometry, 45:553-573, 2011. 10.1007/s00454-010-9319-3.
14. A. Muhammad and A. Jadbabaie. Decentralized computation of homology groups in networks by gossip. In American Control Conference, 2007. ACC 07, pages 3438-3443, july 2007.
15. A. Vergne, L. Decreusefond, and P. Martins. Reduction algorithm for simplicial complexes. In INFOCOM 2013.
16. F. Yan, P. Martins, and L. Decreusefond. Connectivity-based distributed coverage hole detection in wireless sensor networks. In Global Telecommunications Conference (GLOBECOM 2011), 2011 IEEE, pages 1-6, dec. 2011.
17. F. Yan, P. Martins, and L. Decreusefond. Accuracy of homology based approaches for coverage hole detection in wireless sensor networks. In ICC 2012, June 2012.
18. C. Zhang, Y. Zhang, and Y. Fang. Detecting coverage boundary nodes in wireless sensor networks. In Networking, Sensing and Control, 2006. ICNSC 06. Proceedings of the 2006 IEEE International Conference on, pages 868-873, 0-0 2006.
19. A. Zomorodian and G. Carlsson. Computing persistent homology. Discrete & Computational Geometry, 33:249-274, 2005. 10.1007/s00454-004-1146-y.