Coverage in sensor networks via persistent homology

Untitled work

(2001) · Cited by 5,374

Differential Forms in Algebraic Topology

Bott, R., & Tu, L. W. (1982) · Graduate texts in mathematics · doi:10.1007/978-1-4757-3951-0 · Cited by 2,860

Hyperbolic Groups

Gromov, M. (1987) · Mathematical Sciences Research Institute Publications · doi:10.1007/978-1-4613-9586-7_3 · Cited by 1,817

Coverage problems in wireless ad-hoc sensor networks

Meguerdichian, S., Koushanfar, F., Potkonjak, M., & Srivastava, M. B. (2002) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infcom.2001.916633 · Cited by 1,698

Computing Persistent Homology

Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591

Maintaining Sensing Coverage and Connectivity in Large Sensor Networks

Zhang, H., & Hou, J. C. (2005) · Auerbach Publications eBooks · doi:10.1201/9780203323687.ch28 · Cited by 1,509

The Number of Neighbors Needed for Connectivity of Wireless Networks

Xue, F., & Kumar, P. R. (2004) · Wireless Networks · doi:10.1023/b:wine.0000013081.09837.c0 · Cited by 834

Geographic routing without location information

Rao, A., Ratnasamy, S., Papadimitriou, C. H., Shenker, S. J., & Stoica, I. G. (2003) · ACM Annual International Conference on Mobile Computing and Networking (MobiCom) · doi:10.1145/938985.938996 · Cited by 756

Topological persistence and simplification

Edelsbrunner, H., Letscher, D., & Zomorodian, A. J. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2000.892133 · Cited by 716

Coverage in wireless ad hoc sensor networks

Li, X., Wan, P., & Frieder, O. (2003) · IEEE Transactions on Computers · doi:10.1109/tc.2003.1204831 · Cited by 523

A Coupled Alpha Complex

Reani, Y., & Bobrowski, O. (2021) · Journal of computational geometry · doi:10.20382/jocg.v14i1a9 · Cited by 2

$$A_\infty $$ Persistent Homology Estimates Detailed Topology from Pointcloud Datasets

Guillamon, F. B., & Stefanou, A. (2021) · Discrete & Computational Geometry · doi:10.1007/s00454-021-00319-y · Cited by 2

Xenomath!

Stewart, I. (2017) · Springer eBooks · doi:10.1007/978-3-319-61231-7_8 · Cited by 2

0-Dimensional Persistent Homology Analysis Implementation in Resource-Scarce Embedded Systems

Branco, S., Carvalho, J. G., Reis, M. S., Lopes, N. V., & Cabral, J. (2022) · Sensors · doi:10.3390/s22103657 · Cited by 2

Topological Comparison of Some Dimension Reduction Methods Using Persistent Homology on EEG Data

Kwessi, E. A. (2023) · Axioms · doi:10.3390/axioms12070699 · Cited by 2

A homology-based coverage hole detection algorithm in wireless sensor networks

Dong, Y., Kang, H. Y., Yan, F., Shen, L., & Xia, W. (2017) · IEEE International Conference on Computer and Communications (ICCC) · doi:10.1109/compcomm.2017.8322569 · Cited by 2

An Efficient Representation for Filtrations of Simplicial Complexes

Boissonnat, J., & Karthik, C. S. (2017) · ACM-SIAM Symposium on Discrete Algorithms (SODA) · doi:10.1137/1.9781611974782.179 · Cited by 2

Efficient Evader Detection in Mobile Sensor Networks

Adams, H., Ghosh, D., Mask, C., Ott, W., & Williams, K. J. (2025) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/24m1628864 · Cited by 2

Extremal Betti numbers of Rips complexesPreprint

Goff, M. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0910.0040 · Cited by 2

Measuring and Localing Homology ClassesPreprint

Freedman, D., & Chen, C. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0705.3061 · Cited by 2

Hyppo-X : A Scalable Exploratory Framework for Analyzing Complex Phenomics DataPreprint

Kamruzzaman, M., Kalyanaraman, A., Krishnamoorthy, B., Hey, S., & Schnable, P. S. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/159954 · Cited by 2

Decentralized Trajectory Tracking Using Homology and Hodge Decomposition in Sensor NetworksPreprint

Yin, X., Lin, Y.-Y., Ni, C.-C., Ding, J., Han, W., Zhou, D., Gao, J., & Gu, X. D. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1708.09129 · Cited by 2

$A_\infty$ persistent homology estimates the topology from pointcloud datasetsPreprint

Belchí, F., & Stefanou, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1902.09138 · Cited by 2

Through synapses to spatial memory maps: a topological modelPreprint

Dabaghian, Y. A. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.11769 · Cited by 2

Linear-Size Approximations to the Vietoris-Rips FiltrationPreprint

Sheehy, D. R. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1203.6786 · Cited by 2

Topological Data Analysis with $$\epsilon $$-net Induced Lazy Witness Complex

Arafat, N. A., Basu, D., & Bressan, S. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-27618-8_28 · Cited by 1

Bayesian Estimation of Topological Features of Persistence Diagrams

Martínez, A. F. (2022) · Bayesian Analysis · doi:10.1214/22-ba1341 · Cited by 1

Stability for Inference with Persistent Homology Rank Functions

Wang, Q., García‐Redondo, I., Faugère, P., Henselman‐Petrusek, G., & Monod, A. (2024) · Computer Graphics Forum · doi:10.1111/cgf.15142 · Cited by 1

Hierarchical simplicial manifold learning

Zhang, W., Shih, Y.-H., & Li, J.-S. (2024) · PNAS Nexus · doi:10.1093/pnasnexus/pgae530 · Cited by 1

A simplicial homology approach for assessing and rectifying coverage of sensor networks for improved crop management

Rysz, M., Pardalos, P. M., & Mehta, S. S. (2025) · European Journal of Operational Research · doi:10.1016/j.ejor.2025.03.010 · Cited by 1

Probing omics data via harmonic persistent homology

Gurnari, D., Guzmán-Sáenz, A., Utro, F., Bose, A., Basu, S., & Parida, L. (2025) · Scientific Reports · doi:10.1038/s41598-025-12189-y · Cited by 1

Complex Networks: New Models and Distributed Algorithms

Tahbaz-Salehi, A. (2009) · Cited by 1

Distributed computation of a sparse cover in sensor networks without location information

Tahbaz-Salehi, A., & Jadbabaie, A. (2008) · Conference on Information Sciences and Systems · doi:10.1109/ciss.2008.4558716 · Cited by 1

Coordinate-Free Coverage in Sensor Networks via Homology

Iyengar, S. S., Boroojeni, K. G., & Balakrishnan, N. (2014) · Springer eBooks · doi:10.1007/978-1-4419-8420-3_4 · Cited by 1

Versions of Intersection and Local Homology

Bendich, P. L., Harer, J., Saper, L., & Cohen‐Steiner, D. (2008) · Cited by 1

Metric Reconstruction Via Optimal Transport

Adamaszek, M., Adams, H., & Frick, F. (2018) · SIAM Journal on Applied Algebra and Geometry · doi:10.1137/17m1148025 · Cited by 1

Geometric goodness of fit measure to detect patterns in data point clouds

Hernández, A., & Solís, M. (2022) · Computational Statistics · doi:10.1007/s00180-022-01244-1 · Cited by 1

Examine Manipulated Datasets with Topology Data Analysis: A Case Study

Guo, Y. R., Sun, D. W., Li, G., & Chen, S. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-01950-1_21 · Cited by 1

Zigzag zoology

Oudot, S., & Sheehy, D. R. (2013) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/2493132.2462371 · Cited by 1

Persistence landscapes of affine fractals

Catanzaro, M. J., Przybylski, L., & Weber, E. (2022) · Demonstratio Mathematica · doi:10.1515/dema-2022-0015 · Cited by 1

Packing Problem and Random Coverage in Continuous Domain

Nandi, M. (2023) · Asian Journal of Research in Computer Science · doi:10.9734/ajrcos/2023/v16i3347 · Cited by 1

Topological Spaces

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.002 · Cited by 1

Structural-Order Analysis Based on Applied Mathematics

Shiga, M., & Obayashi, I. (2023) · The Materials Research Society series · doi:10.1007/978-981-99-5235-9_11 · Cited by 1

Adaptive approximation of persistent homology

Herick, M., Joachim, M., & Vahrenhold, J. (2024) · Journal of Applied and Computational Topology · doi:10.1007/s41468-024-00192-7 · Cited by 1

Quantum distance approximation for persistence diagrams

Ameneyro, B., Herrman, R., Siopsis, G., & Maroulas, V. (2024) · Journal of Physics Complexity · doi:10.1088/2632-072x/ad9fca · Cited by 1

Spatial AI in Robotics and Spatial Computing

Papadimitriou, F. (2025) · SpringerBriefs in applied sciences and technology · doi:10.1007/978-3-031-82136-3_4 · Cited by 1

Decentralized Computation of Homology in Wireless Sensor Networks Using Spanning Trees

Šoberl, D., Kosta, N. M., & Škraba, P. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-66808-6_3 · Cited by 1

Extracting Topological Features from Big Data Using Persistent Density Entropy

Xu, J., Li, X., & Wang, H. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1168/3/032017 · Cited by 1

Coverage Assessment and Target Tracking in 3D Domains

Iyengar, S. S., Boroojeni, K. G., & Balakrishnan, N. A. (2014) · Springer eBooks · doi:10.1007/978-1-4419-8420-3_5 · Cited by 1

Reduction algorithm for random abstract simplicial complexesPreprint

Decreusefond, L., Martins, P., & Vergne, A. (2013) · arXiv (Cornell University) · Cited by 1

Asymptotic Stability of Switched Higher Order Laplacians

Muhammad, A., & Jadbabaie, A. (2007) · Springer eBooks · doi:10.1007/978-3-540-71493-4_70 · Cited by 1

Nearest Prime Simplicial Complex for Object RecognitionPreprint

Zhang, J., Xie, Z., & Li, S. Z. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1106.0987 · Cited by 1

Cyclic network automata and cohomological wavesPreprint

Cai, Y., & Ghrist, R. (2014) · doi:10.5555/2602339.2602363 · Cited by 1

Exploratory Nuclear Reactor Safety Analysis and Visualization via Integrated Topological and Geometric Techniques

Idaho National Lab. (INL), I. F., Maljovec, D., USDOE, Wang, B., Pascucci, V., Bremer, P., Mandelli, D., Pernice, M., & Nourgaliev, R. R. (2013) · doi:10.2172/1117729 · Cited by 1

Stable comparison of multidimensional persistent homology groups with torsionPreprint

Frosini, P. (2010) · AMS Acta (University of Bologna) · doi:10.48550/arxiv.1012.4169 · Cited by 1

Quantales, persistence, and magnitude homologyPreprint

Cho, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.02905 · Cited by 1

An Excision Theorem for Persistent HomologyPreprint

Palser, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.03348 · Cited by 1

Topology of nerves and formal conceptsPreprint

Ayzenberg, A. A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.05491 · Cited by 1

Topological Data Analysis for Clustering and Classifying Time Series

Chen, R. (2019) · OpenCommons at University of Connecticut (University of Connecticut) · Cited by 1

Persistence Homology of TEDtalk: Do Sentence Embeddings Have a Topological Shape?Preprint

Das, S., Haque, S. A., & Tanveer, M. I. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.14131 · Cited by 5

Noise robustness of persistent homology on greyscale images, across filtrations and signaturesPreprint

s, R. T. V., Nys, J., Verdonck, T., & e, S. L. '. (2021) · arXiv (Cornell University) · Cited by 1

A Metric for Tree-Like Topological SummariesPreprint

Pegoraro, M. (2021) · arXiv (Cornell University) · Cited by 1

(Thesis) Reservoir Computing With Dynamical SystemsPreprint

Hart, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.14226 · Cited by 2

Index

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.014 · Cited by 1

Interpreting topology in the context of social science

Feng, M. (2025) · Proceedings of symposia in applied mathematics · doi:10.1090/psapm/080/00731 · Cited by 1

Optimisation de la couverture de communication et de mesure dans les réseaux de capteurs

Zhang, M. (2015) · theses.fr (ABES) · doi:10.70675/12fc1af4zc66ez43b3z8b0dzb81ae83b232f · Cited by 1

Characterizing Obstacle-Avoiding Paths Using Cohomology Theory

Dłotko, P., Kropatsch, W. G., & Wagner, H. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-23672-3_38

Cyclic Cellular Automata on Networks and Cohomological Waves

Cai, Y. (2013) · ScholarlyCommons (University of Pennsylvania)

Data-inspired advances in geometric measure theory: generalized surface and shape metricsPreprint

Ibrahim, S. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1408.5954

Stochastic Homology. Reduction Formulas for Computing Stochastic Betti Numbers of Maximal Random Complexes with Discrete Probabilities. Computation and ApplicationsPreprint

Тодоров, Т. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1107.0859

Computing interesting topological features

Erickson, J., & Chambers, E. W. (2008)

Consensus formation on a simplicial complex of opinions

Maletić, S., & Rajković, M. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.12.001

LDRD 149045 final report distinguishing documents.

Mitchell, S. A. (2010) · doi:10.2172/1008125

Computing Persistent Homology via Discrete Morse Theory

Mller, J. M., & Winter, P. (2013)

Coverage Criterion in Sensor Networks Stable under PerturbationPreprint

Hiraoka, Y., & Kusano, G. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1409.7483

Algorithms and hardness results in computational homology

Freedman, D. Z., & Chen, C. (2009)

Control of Multi-Agent Networks: From Network Design to Decentralized Coordination

Twu, P. (2012) · SMARTech Repository (Georgia Institute of Technology)

Ranking Entities in Networks via Lefschetz Duality

Aabrandt, A., Hansen, V. L., Poulsen, B., & Træholt, C. (2014) · UKSim European Symposium on Computer Modeling and Simulation (EMS) · doi:10.1109/ems.2014.17

An Algorithmic Way to Generate Simplexes for Topological Data Analysis

Rykaczewski, K., Wiśniewski, P., & Stencel, K. (2016) · CS&P

A topology-based approach for feature extraction from 3D motion gesture

Nakada, K., & Miura, K. (2017) · IEEE International Workshop on Computational Intelligence and Applications (IWCIA) · doi:10.1109/iwcia.2017.8203587

Describing and Mapping the Interactions between Student Affective Factors Related to Persistence in Science, Physics, and Engineering

Doyle, J. (2017) · FIU - Digital Commons (Florida International University) · doi:10.25148/etd.fidc001978

Topological data analysis and the MAA national study of college calculus

Stevens, I. E. (2016)

Random coverings of 1-complexes and the Euler characteristicPreprint

Komendarczyk, R., & Pullen, J. K. (2012) · arXiv (Cornell University)

Topological data analysis: applications in machine learning

Calcina, S. G. S. (2019) · doi:10.11606/t.55.2019.tde-03012019-094950

Methods in Homology Inference

Cavanna, N. J. (2019) · OpenCommons - UConn (University of Connecticut)

Topologia computacional para análise de série temporal

Miranda, V. L. D. (2019) · doi:10.11606/d.59.2019.tde-13052019-175021

Discrete Morse theory for computing cellular sheaf cohomologyPreprint

Curry, J. M., Ghrist, R., & Nanda, V. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1312.6454

Cyclic network automata and cohomological waves

Cai, Y., & Ghrist, R. (2014) · ACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN) · doi:10.1109/ipsn.2014.6846754

Study on Base Station Topology in National Cellular Networks: Take Advantage of Alpha Shapes, Betti Numbers, and Euler Characteristics

Chen, Y., Li, R., Zhao, Z., & Zhang, H. (2019) · IEEE Systems Journal · doi:10.1109/jsyst.2019.2920658

Random \v{C}ech complexes on $\mathbb{R}^d$: decrackling the noise with local scalingsPreprint

de Kergorlay, H. (2019) · arXiv (Cornell University)

Persistent Homology Techniques for Big Data and Machine Intelligence: A Survey

Joshi, M. A., Joshi, D., & Sharma, V. S. (2020) · Advances in intelligent systems and computing · doi:10.1007/978-981-15-1366-4_8

ROBUST FIXED-TIME CONSENSUS PROTOCOLS FOR MULTI-AGENT SYSTEMS WITH NONLINEAR STATE MEASUREMENTS

Ye, C., Shi, B., & Wu, B. (2020) · Journal of Applied Analysis & Computation · doi:10.11948/20190208

Estimation of first-order sensitivity indices based on symmetric reflected Vietoris-Rips complexes areasPreprint

Hernández, A., Solís, M., & Zúñiga-Rojas, R. A. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.05351

Convergence of persistence diagram in the subcritical regimePreprint

Owada, T. (2021) · arXiv (Cornell University)

Consensus of a two-agent system with nonlinear dynamics and time-varying delay

Ye, C., Shi, B., & Ding, L. (2021) · Applications of Mathematics · doi:10.21136/am.2021.0341-19

Efficient Evolutionary Models with DigraphonsPreprint

Tamaskar, A., & Mishra, B. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2104.12748

Analysis of Spatiotemporal Anomalies Using Persistent Homology: Case Studies with COVID-19 Data.Preprint

Hickok, A., Needell, D. M., & Porter, M. A. (2021) · arXiv (Cornell University)

A Method for Detection of Local Dimension in Point Cloud Data

Boersma, C. (2017) · doi:10.31979/etd.5dws-69vv

Homology I: Simplicial Complexes to Sensor Networks

Schenck, H. (2022) · Mathematics of data · doi:10.1007/978-3-031-06664-1_4

Existence and uniqueness of solutions to the norm minimum problem on digraphs

Wang, C. (2022) · Open Mathematics · doi:10.1515/math-2022-0495

Estimating the Coverage Measure and the Area Explored by a Line-Sweep Sensor on the PlanePreprint

Vianna, M. L. C., Goubault, É., Jaulin, L., & Putot, S. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2309.03604

Triangulation of Submanifolds

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.008

Good Triangulations

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.006

Delaunay Complexes

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.005

Stability of Distance Functions

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.010

Delaunay Filtrations

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.007

Simplicial Complexes

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.003

Homology Inference

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.012

Bibliography

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.013

Reconstruction of Submanifolds

Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.009

Coverage and hole-detection in sensor networks via homology

Ghrist, R., & Muhammad, A. (2005) · International Symposium on Information Processing in Sensor Networks (IPSN) · doi:10.1109/ipsn.2005.1440933 · Cited by 293

Coverage Verification Algorithm for Sensor Networks

Ćwiszewski, A., & Wiśniewski, P. (2012) · Communications in computer and information science · doi:10.1007/978-3-642-35521-9_58 · Cited by 2

Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology

de Silva, V., & Ghrist, R. (2006) · The International Journal of Robotics Research · doi:10.1177/0278364906072252 · Cited by 198

Coordinate-Free Coverage in Sensor Networks via Homology

Iyengar, S. S., Boroojeni, K. G., & Balakrishnan, N. (2014) · Springer eBooks · doi:10.1007/978-1-4419-8420-3_4 · Cited by 1

Mayer–Vietoris sequences and coverage problems in sensor networks

Arai, Z., Hayashi, K., & Hiraoka, Y. (2011) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/s13160-011-0039-8 · Cited by 8