In this paper, we present three distributed algorithms for coverage verification in sensor networks with no location information. We demonstrate how, in the absence of localization …
Algebraic topology is one of the most important creations in mathematics which uses algebraic tools to study topological spaces. The basic goal is to find algebraic invariants that …
Fix a finite set of points in Euclidean n-space E^n, thought of as a point-cloud sampling of a certain domain D⊂E^n. The Vietoris–Rips complex is a combinatorial simplicial complex …
NO Malott, S Chen, PA Wilsey - IEEE Transactions on …, 2022 - ieeexplore.ieee.org
Persistent Homology is a computational method of data mining in the field of Topological Data Analysis. Large-scale data analysis with persistent homology is computationally …
With the aim to generalize the theory of Lp and L π de Rham cohomology to metric measure spaces, we define the scaled Alexander-Spanier cohomology and Lp and L π Alexander …
TK Dey, K Li - Proceedings of the twenty-fifth annual symposium on …, 2009 - dl.acm.org
A cut locus of a point p in a compact Riemannian manifold M is defined as the set of points where minimizing geodesics issued from p stop being minimizing. It is known that a cut locus …
Z Arai, K Hayashi, Y Hiraoka - Japan journal of industrial and applied …, 2011 - Springer
A coverage problem of sensor networks is studied. Following recent works by Ghrist et al., in which computational topological methods are applied for the coverage problem, We present …
D Eppstein - arXiv preprint arXiv:0909.1866, 2009 - arxiv.org
We describe a data structure, a rectangular complex, that can be used to represent hyperconvex metric spaces that have the same topology (although not necessarily the same …
In this paper we generalize work using topological methods for testing wireless/sensor network coverage to the problem of covering a geographically-distributed wireless network …