Coverage in sensor networks via persistent homology

By Vin de Silva, Robert Ghrist. 2007

489 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/25b68dffcca670674b33b513a4817517b43e9f24

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Betti numbers in multidimensional persistent homology are stable functions (2013, background): “, [8, 9, 29, 34]) to data simplification [21 ] and hole detection in sensor networks [15].”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “Simplicial complex models have been successful in developing new insights into biological data [32, 92], structural and functional connectivity in the brain [57,58,104], coverage of sensor networks [42,56,90,121], signal processing [8,115], mobility analysis [54], and robotics [105].”
A roadmap for the computation of persistent homology (2015, background): “…(TDA) [21] have provided a wealth of new insights in the study of data in an increasingly diverse set of applications — including coverage in sensor networks [37], protein structure [56,77,126], stability of fullerene molecules [125], robotics [10, 105, 119], signals in images [29, 65],…”
Persistent homology for random fields and complexes (2010, background): “Recent excellent and quite different reviews by Carlsson [10, 13], Edelsbrunner and Harer [20], and Ghrist [1, 17, 18, 23] give a broad exposition of the basics of persistent homology.”
Barcodes: The persistent topology of data (2007, background): “1 (de Silva [10]).”
Topological complexity of smooth random functions (2011, background): “A very lively discussion of this trend can be found in Rob Ghrist’s review [40], book in progress [41] and website on a project on sensor topology for minimal planning [42].”
Maximally Persistent Cycles in Random Geometric Complexes (2015, background): “For subsets of Euclidean space, the constant 2 can be improved (see [25]).”
Classifying Clustering Schemes (2010, background): “Moreover, the functoriality of the construction of path-connected components is a key feature in all aspects of topology, and the functoriality of clustering constructions should play a similar role in the computational topology of ﬁnite datasets [3, 8, 9, 11, 12].”
Topological Consistency via Kernel Estimation (2014, unknown): “√ In addition, it is shown in [20] that R ( X , r ) ⊂ C ( X , 2 r ).”