Volume 7, issue 1 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Coverage in sensor networks via persistent homology

Vin de Silva and Robert Ghrist

Algebraic & Geometric Topology 7 (2007) 339–358
1 M Allili, K Mischaikow, A Tannenbaum, Cubical homology and the topological classification of 2D and 3D imagery, from: "IEEE Intl. Conf. Image Proc." (2001) 173
2 A Ames, A homology theory for hybrid systems: hybrid homology, Lect. Notes in Computer Science 3414 (2005) 86
3 R Bott, L W Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer (1982) MR658304
4 V de Silva, Plex
5 V d Silva, G Carlsson, Topological estimation using witness complexes, Symp. Point-Based Graphics (2004)
6 V d Silva, R Ghrist, Coordinate-free coverage in sensor networks with controlled boundaries, Int. J. Robotics Research 25 (2006) 1205
7 V d Silva, R Ghrist, A Muhammad, Blind swarms for coverage in 2–d, from: "Robotics: Systems and Science" (2005)
8 J Eckhoff, Helly, Radon, and Carathéodory type theorems, from: "Handbook of convex geometry, Vol. A, B", North-Holland (1993) 389 MR1242986
9 H Edelsbrunner, D Letscher, A Zomorodian, Topological persistence and simplification, from: "41st Annual Symposium on Foundations of Computer Science (Redondo Beach, CA, 2000)", IEEE Comput. Soc. Press (2000) 454 MR1931842
10 S Fekete, A Kröller, D Pfisterer, S Fischer, Deterministic boundary recognition and topology extraction for large sensor networks (2006)
11 M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
12 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
13 J C Hausmann, On the Vietoris–Rips complexes and a cohomology theory for metric spaces, from: "Prospects in topology (Princeton, NJ, 1994)", Ann. of Math. Stud. 138, Princeton Univ. Press (1995) 175 MR1368659
14 T Kaczynski, K Mischaikow, M Mrozek, Computational homology, Applied Mathematical Sciences 157, Springer (2004) MR2028588
15 H Koskinen, On the coverage of a random sensor network in a bounded domain, from: "Proceedings of 16th ITC Specialist Seminar" (2004) 11
16 X Y Li, P J Wan, O Frieder, Coverage in wireless ad-hoc sensor networks, IEEE Transaction on Computers 52 (2003) 753
17 B Liu, D Towsley, A study of the coverage of large-scale sensor networks, from: "IEEE International Conference on Mobile Ad-hoc and Sensor Systems" (2004)
18 S Meguerdichian, F Koushanfar, M Potkonjak, M Srivastava, Coverage problems in wireless ad-hoc sensor network, from: "IEEE INFOCOM" (2001) 1380
19 K Mischaikow, M Mrozek, J Reiss, A Szymczak, Construction of symbolic dynamics from experimental time series, Phys. Rev. Lett. 82 (1999) 1144
20 A Rao, C Papadimitriou, S Shenker, I Stoica, Geographic Routing without Location Information, from: "Proceedings of 9th Annual International Conference on Mobile Computing and Networking (Mobicom'03)" (2003)
21 L Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann. 97 (1927) 454 MR1512371
22 F Xue, P R Kumar, The number of neighbors needed for connectivity of wireless networks, Wireless Networks 10 (2004) 169
23 H Zhang, J Hou, Maintaining Coverage and Connectivity in Large Sensor Networks, from: "International Workshop on Theoretical and Algorithmic Aspects of Sensor, Ad hoc Wireless and Peer-to-Peer Networks" (2004)
24 A Zomorodian, G Carlsson, Computing persistent homology, Discrete Comput. Geom. 33 (2005) 249 MR2121296