Complexity of simplicial homology and independence com495 plexes of chordal graphs, Computational Geometry: Theory and Applications, vol.57, pp.8-18, 2016. ,
Efficient data structure for representing and sim498 plifying simplicial complexes in high dimensions, International Journal of Computational 499 Geometry and Applications (IJCGA), vol.22, pp.279-303, 2012. ,
Strong homotopy types, nerves and collapses. Discrete 501 and Computational Geometry, vol.47, pp.301-328, 2012. ,
Clear and compress: Computing persistent 503 homology in chunks, Topological Methods in Data Analysis and Visualization III, Math504 ematics and Visualization, pp.103-117, 2014. ,
,
Building efficient and 507 compact data structures for simplicial complexes, Algorithmica, vol.79, pp.530-567, 2017. ,
, Siddharth Pritam, and Divyansh Pareek. Strong Collapse for, p.509
, 26th Annual European Symposium on Algorithms (ESA 2018), vol.112, 2018.
, XX:14 Computing Persistent Homology of Flag Complexes via Strong Collapses
An efficient representation for filtrations of 512 simplicial complexes, ACM-SIAM Symposium on Discrete Algorithms (SODA, 2017. ,
Approximating persistent homology in euclidean space 514 through collapses, Applicable Algebra in Engineering, vol.515, pp.73-101 ,
Zigzag persistence, Found Comput Math, vol.10, 2010. ,
Zigzag persistent homology and 518 real-valued functions. SOCG, pp.247-256, 2009. ,
On the local be520 havior of spaces of natural images, International Journal of Computer Vision, vol.76, pp.1-12, 2008. ,
Topology of viral evolution ,
, Proceedings of the National Academy of Sciences, vol.110, issue.524, pp.18566-18571, 2013.
Towards persistence-based reconstruction in euclidean spaces ,
URL : https://hal.archives-ouvertes.fr/inria-00197543
, , 2008.
Persistent homology computation with a twist, European 527 Workshop on Computational Geometry (EuroCG), pp.197-200, 2011. ,
, Polynomial-Sized To529 pological Approximations Using The Permutahedron. 32nd International Symposium on 530 Computational Geometry (SoCG), 2016.
Harer,john. stability of persistence 532 diagrams, Discrete Comput. Geom, vol.37, pp.103-120, 2007. ,
,
Coverage in sensor networks via persistent homology, 535 Algebraic and Geometric Topology, vol.7, pp.339-358, 2007. ,
Quiver representations. Notices of the American Math537 ematical Society, vol.52, pp.200-206, 2005. ,
Computing topological persistence for simplicial maps, 539 Symposium on Computational Geometry (SoCG, pp.345-354, 2014. ,
Topology preserving edge con541 traction, Publications de l'Institut Mathematique (Beograd), vol.60, pp.23-45, 1999. ,
SimBa: An efficient tool for approximating Rips543 filtration persistence via Simplicial Batch-collapse, European Symp. on Algorithms 544 (ESA), vol.35, pp.1-35, 2016. ,
Homology groups of relations, The Annals of Mathematics, vol.56, p.546, 1952. ,
Simplification of complexes for persistent homology computa547 tions, Homology, Homotopy and Applications, vol.16, pp.49-63, 2014. ,
Topological persistence and simplifica549 tion, Discrete Comput. Geom, vol.28, pp.511-533, 2002. ,
Computational Topology: An Introduction, 2010. ,
Introduction to the r 553 package tda, 2014. ,
Foldings in graphs and relations with simplicial complexes and 555 posets, Discrete Mathematics, issue.17, pp.2639-2651, 2012. ,
Powers of tensors and fast matrix multiplication, vol.14, pp.296-303, 2014. ,
, Gudhi: Geometry understanding in higher dimensions
Algebraic Topology, 2001. ,
, , p.15
Barcodes of towers and a streaming algorithm 562 for persistent homology, 33rd International Symposium on Computational Geometry, vol.563, 2017. ,
Approximate ?ech complex in low and high dimen565 sions, Algorithms and Computation, vol.8283, pp.666-676, 2013. ,
Zigzag persistence via reflections and transpositions, Proc ,
URL : https://hal.archives-ouvertes.fr/hal-01091949
, ACM-SIAM Symposium on Discrete Algorithms (SODA) pp, pp.181-199, 2015.
Zigzag persistent homology in 570 matrix multiplication time, Symposium on Computational Geometry (SoCG), p.571, 2011. ,
Morse theory for filtrations and efficient computation of 572 persistent homology, vol.50, pp.330-353, 2013. ,
,
Elements of Algebraic Topology, 1984. ,
A roadmap for the 576 computation of persistent homology, EPJ Data Science, p.17, 2017. ,
A klein-bottle-based dictionary for texture representation ,
, International Journal of Computer Vision, vol.107, pp.75-97, 2014.
,
Linear-size approximations to the vietoris-rips filtration. Discrete and 581 Computational Geometry, vol.49, pp.778-796, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01111878
Recognition of collapsible complexes is np-complete. Discrete and Computa583 tional Geometry, vol.55, pp.21-38, 2016. ,
Phat-persistent homology algorithms 585 toolbox, Journal of Symbolic Computation, vol.78, 2017. ,
Simplicial spaces nuclei and m-groups, Proc. London Math. Soc, vol.587, pp.243-327, 1939. ,
Computing persistent features in big data: 589 A distributed dimension reduction approach, ICASSP-Proceedings, p.590, 2014. ,
Simplifying the homology of 591 networks via strong collapses, ICASSP-Proceedings, 2013. ,
Computing persistent homology, Discrete Comput. Geom, vol.593, pp.249-274, 2005. ,