An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Connecting the Physical World with Pervasive Networks
IEEE Pervasive Computing
ICDCS '01 Proceedings of the The 21st International Conference on Distributed Computing Systems
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
The coverage problem in a wireless sensor network
WSNA '03 Proceedings of the 2nd ACM international conference on Wireless sensor networks and applications
The number of neighbors needed for connectivity of wireless networks
Wireless Networks
Network coverage using low duty-cycled sensors: random & coordinated sleep algorithms
Proceedings of the 3rd international symposium on Information processing in sensor networks
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On k-coverage in a mostly sleeping sensor network
Proceedings of the 10th annual international conference on Mobile computing and networking
Localization and Navigation Assisted by Networked Cooperating Sensors and Robots
International Journal of Robotics Research
Distributed environmental monitoring using random sensor networks
IPSN'03 Proceedings of the 2nd international conference on Information processing in sensor networks
A homology theory for hybrid systems: hybrid homology
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Coverage in wireless ad hoc sensor networks
IEEE Transactions on Computers
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
Robust and Efficient Covering of Unknown Continuous Domains with Simple, Ant-Like A(ge)nts
International Journal of Robotics Research
Fine-grained boundary recognition in wireless ad hoc and sensor networks by topological methods
Proceedings of the tenth ACM international symposium on Mobile ad hoc networking and computing
Algebraic approach to recovering topological information in distributed camera networks
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
Multiagent coverage algorithms with gossip communication: control systems on the space of partitions
ACC'09 Proceedings of the 2009 conference on American Control Conference
Asymptotic stability of switched higher order laplacians
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
On the Topology of Discrete Strategies
International Journal of Robotics Research
A distributed topological camera network representation for tracking applications
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
A multi-robot exploration algorithm based on a static Bluetooth communication chain
Robotics and Autonomous Systems
Efficient algorithms for distributed detection of holes and boundaries in wireless networks
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Perimeter detection in wireless sensor networks
Robotics and Autonomous Systems
Failure filtrations for fenced sensor networks
International Journal of Robotics Research
| Hi-index | 0.01 |
Tools from computational homology are introduced to verify coverage in an idealized sensor network. These methods are unique in that, while they are coordinate-free and assume no localization or orientation capabilities for the nodes, there are also no probabilistic assumptions. The key ingredient is the theory of homology from algebraic topology. The robustness of these tools is demonstrated by adapting them to a variety of settings, including static planar coverage, 3-D barrier coverage, and time-dependent sweeping coverage. Results are also given on hole repair, error tolerance, optimal coverage, and variable radii. An overview of implementation is given.