Distributed computation of coverage in sensor networks by homological methods

Dłotko, Paweł; Ghrist, Robert; Juda, Mateusz; Mrożek, Marian

doi:10.1007/s00200-012-0167-7

Cited by 48 publications

(28 citation statements)

References 28 publications

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“…The last two decades have witnessed a rapid growth in the range of applications of algebraic topology including sensor networks, image analysis, data analysis, material science and nonlinear dynamics [20,13,5,12,16,15,28,10,9,29].…”

Section: Introductionmentioning

confidence: 99%

Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps

et al. 2013

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We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic pre-processing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function.

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Section: Introductionmentioning

confidence: 99%

Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps

et al. 2013

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“…As regards implementation in real WSN, these homology based methods are necessarily centralized, which makes them impractical in large scale sensor networks. Some algorithms have been proposed to implement the above mentioned ideas in a distributed context, see [9]- [11].…”

Section: Introductionmentioning

confidence: 99%

Accuracy of homology based approaches for coverage hole detection in wireless sensor networks

Yan

Martins

Decreusefond

2012

2012 IEEE International Conference on Communications (ICC)

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Abstract-Homology theory provides new and powerful solutions to address the coverage problems in wireless sensor networks (WSNs). They are based on algebraic objects, such asČech complex and Rips complex.Čech complex gives accurate information about coverage quality but requires a precise knowledge of the relative locations of nodes. This assumption is rather strong and hard to implement in practical deployments.

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“…These include new algorithms that use graph theoretic approaches [125] for computing, maintaining or maximizing connectivity [126,127,128], controllability [129], and robustness of coordinated motion to uncertainty [130]. Techniques from algebraic topology have also been applied to problems in multi-vehicle sensing [131]. Advances in cooperative routing and motion planning for multiple autonomous vehicles have been extensive, see for example [132,133].…”

Section: Recent Developments and Future Directionsmentioning

confidence: 99%

Cooperative Vehicle Environmental Monitoring

Leonard

2016

Springer Handbook of Ocean Engineering

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Over the last decade, methodologies for automated cooperative control of robotic vehicles have been designed, deployed and proven to provide efficient, reliable, and sustained monitoring of the uncertain and inhospitable ocean environment. Unprecedented data sets have been collected from deployments of cooperative vehicles in the field, and both real-time and post-deployment analyses have led to new understanding of the environment. This first decade of success in cooperative vehicle environmental monitoring sets the stage for new opportunities and future gain, especially as the development of cooperative control methodologies can continue to leverage ongoing technological and scientific advances in underwater communication and sensing, energy and computational efficiency, vehicle size, speed, maneuverability and cost, and ocean modeling and prediction.Indeed, the demonstrated potential of cooperative vehicle control has led to increased demand for fleets of autonomous underwater vehicles (AUVs) for use in measuring ocean physics, biology, chemistry and geology to improve understanding of natural dynamics and human-influenced changes in the marine environment. Further, methodologies for cooperative control of robotic vehicles in the ocean are readily adaptable to applications on land, in the air and in space; likewise, there is much to be learned from developments in these other domains. The recent explosion in research on networks and complex systems, including investigation of mechanisms that explain a "collective intelligence" exhibited by animal aggregations on the move, are also being leveraged to advance design of cooperative vehicle dynamics.For environmental monitoring to be successful, physical, chemical, and biological variables must be measured across a range of spatial and temporal scales; in the ocean the monitoring strategy must also contend with a harsh, three-dimensional physical space that is highly uncertain and dynamic. Small spatial and temporal scales associated with the measured variables typically make a stationary sensor array impractical because a very large number of sensors would be needed to get sufficient resolution in space and/or time. An array of mobile sensors, however, may be very well suited to such a challenge since mobility can be exploited to dynamically distribute fewer sensors according to the spatial and temporal scales.The underlying principle of cooperative control of vehicles for environmental monitoring leverages mobility of sensors and uses an interacting dynamic among the individual sensors to yield a collective behavior that performs better than the sum of the parts. If the vehicles can communicate their state or measure the relative state of others in the team, then they can cooperate and the cooperative vehicle dynamics can provide coordinated motion of the team as a whole. The resulting vehicle network functions as a dynamically reconfigurable sensor array with a capability for high performance in environmental monitoring not available at the level of individual...

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Distributed computation of coverage in sensor networks by homological methods

Cited by 48 publications

References 28 publications

Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps

Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps

Accuracy of homology based approaches for coverage hole detection in wireless sensor networks

Cooperative Vehicle Environmental Monitoring

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