M. Adamaszek and J. Stacho, Complexity of simplicial homology and independence complexes of chordal graphs, Computational Geometry: Theory and Applications, vol.57, pp.8-18, 2016.

D. Attali, A. Lieutier, and D. Salinas, Efficient data structure for representing and simplifying simplicial complexes in high dimensions, International Journal of Computational Geometry and Applications (IJCGA), vol.22, pp.279-303, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00579902

J. A. Barmak and E. G. Minian, Strong homotopy types, nerves and collapses. Discrete and Computational Geometry, vol.47, pp.301-328, 2012.

U. Bauer and . Ripser,

U. Bauer, M. Kerber, and J. Reininghaus, Clear and compress: Computing persistent homology in chunks, Topological Methods in Data Analysis and Visualization III, Mathematics and Visualization, pp.103-117, 2014.

U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, PHAT -persistent homology algorithms toolbox, Journal of Symbolic Computation, vol.78, 2017.

J. Boissonnat and C. S. Karthik, An efficient representation for filtrations of simplicial complexes, ACM-SIAM Symposium on Discrete Algorithms (SODA, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01416683

J. Boissonnat, S. Pritam, and D. Pareek, Strong Collapse for Persistence, 26th Annual European Symposium on Algorithms (ESA 2018), vol.112, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01886165

M. Botnan and G. Spreemann, Approximating persistent homology in euclidean space through collapses, Applicable Algebra in Engineering, Communication and Computing, vol.26, pp.73-101

G. Carlsson and V. Silva, Zigzag persistence, Found Comput Math, vol.10, 2010.

G. Carlsson, V. Silva, and D. Morozov, Zigzag persistent homology and real-valued functions. SOCG, pp.247-256, 2009.

G. Carlsson, T. Ishkhanov, V. Silva, and A. Zomorodian, On the local behavior of spaces of natural images, International Journal of Computer Vision, vol.76, pp.1-12, 2008.

J. M. Chan, G. Carlsson, and R. Rabadan, Topology of viral evolution, Proceedings of the National Academy of Sciences, vol.110, pp.18566-18571, 2013.

F. Chazal and S. Oudot, Towards persistence-based reconstruction in euclidean spaces, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00197543

C. Chen and M. Kerber, Persistent homology computation with a twist, European Workshop on Computational Geometry (EuroCG), pp.197-200, 2011.

A. Choudhary, M. Kerber, and S. Raghvendra, Polynomial-Sized Topological Approximations Using The Permutahedron. 32nd International Symposium on Computational Geometry (SoCG), 2016.

H. Edelsbrunner, D. Cohen-steiner, and J. Harer, Stability of persistence diagrams. Discrete and Compututaional Geometry, vol.37, pp.103-120, 2007.

. Datasets and . Url,

V. Silva and R. Ghrist, Coverage in sensor networks via persistent homology, Algebraic and Geometric Topology, vol.7, pp.339-358, 2007.

H. Derksen and J. Weyman, Quiver representations. Notices of the, vol.52, pp.200-206, 2005.

T. K. Dey, H. Edelsbrunner, S. Guha, and D. Nekhayev, Topology preserving edge contraction, Publications de l'Institut Mathematique (Beograd), vol.60, pp.23-45, 1999.

T. K. Dey, F. Fan, and Y. Wang, Computing topological persistence for simplicial maps, Symposium on Computational Geometry (SoCG, pp.345-354, 2014.

T. K. Dey, D. Shi, and Y. Wang, SimBa: An efficient tool for approximating Rips-filtration persistence via Simplicial Batch-collapse, European Symp. on Algorithms (ESA), vol.35, pp.1-35, 2016.

T. K. Dey and R. Slechta, Filtration simplification for persistent homology via edge contraction, International Conference on Discrete Geometry for Computer Imagery, 2019.

C. H. Dowker, Homology groups of relations, The Annals of Mathematics, vol.56, pp.84-95, 1952.

P. D?otko and H. Wagner, Simplification of complexes for persistent homology computations, Homology, Homotopy and Applications, vol.16, pp.49-63, 2014.

H. Edelsbrunner and J. Harer, Computational Topology: An Introduction, 2010.

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and simplification. Discrete and Compututational Geometry, vol.28, pp.511-533, 2002.

B. T. Fasy, J. Kim, F. Lecci, and C. Maria, Introduction to the r package tda, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01113028

E. Fieux and J. Lacaze, Foldings in graphs and relations with simplicial complexes and posets, Discrete Mathematics, vol.55, issue.17, p.15, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00769072

F. and L. Gall, Powers of tensors and fast matrix multiplication, vol.14, pp.296-303, 2014.

, Gudhi: Geometry understanding in higher dimensions

A. Hatcher, Algebraic Topology, 2001.

C. S. Karthik, J. Boissonnat, and S. Tavenas, Building efficient and compact data structures for simplicial complexes, Algorithmica, vol.79, pp.530-567, 2017.

M. Kerber and H. Schreiber, Barcodes of towers and a streaming algorithm for persistent homology, 33rd International Symposium on Computational Geometry, 2017.

M. Kerber and R. Sharathkumar, Approximate ?ech complex in low and high dimensions, Algorithms and Computation, vol.8283, pp.666-676, 2013.

C. Maria and S. Oudot, Zigzag persistence via reflections and transpositions, Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA) pp, pp.181-199, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01091949

N. Milosavljevic, D. Morozov, and P. Skraba, Zigzag persistent homology in matrix multiplication time, Symposium on Computational Geometry (SoCG), 2011.
URL : https://hal.archives-ouvertes.fr/inria-00520171

K. Mischaikow and V. Nanda, Morse theory for filtrations and efficient computation of persistent homology. Discrete and Computational Geometry, vol.50, pp.330-353, 2013.

D. Mozozov and . Dionysus,

J. Munkres, Elements of Algebraic Topology, 1984.

N. Otter, M. Porter, U. Tillmann, P. Grindrod, and H. Harrington, A roadmap for the computation of persistent homology, EPJ Data Science, p.17, 2017.

J. Perea and G. Carlsson, A Klein-bottle-based dictionary for texture representation, International Journal of Computer Vision, vol.107, pp.75-97, 2014.

H. Schreiber and . Sophia,

D. Sheehy, Linear-size approximations to the Vietoris-Rips filtration. Discrete and Computational Geometry, vol.49, pp.778-796, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01111878

M. Tancer, Recognition of collapsible complexes is NP-complete. Discrete and Computational Geometry, vol.55, pp.21-38, 2016.

J. H. Whitehead, Simplicial spaces nuclei and m-groups, Proc. London Math. Soc, vol.45, pp.243-327, 1939.

A. C. Wilkerson, H. Chintakunta, and H. Krim, Computing persistent features in big data: A distributed dimension reduction approach, International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp.11-15, 2014.

A. C. Wilkerson, T. J. Moore, A. Swami, and A. H. Krim, Simplifying the homology of networks via strong collapses, International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp.11-15, 2013.

A. Zomorodian, The tidy set: A minimal simplicial set for computing homology of clique complexes, Proceedings of the Twenty-sixth Annual Symposium on Computational Geometry, pp.257-266, 2010.

A. Zomorodian and G. Carlsson, Computing persistent homology. Discrete and Computational Geometry, vol.33, pp.249-274, 2005.