bibliography.bib

@inproceedings{gudhilibrary_ICMS14,
  author    = {Cl\'ement Maria and Jean-Daniel Boissonnat and 
              Marc Glisse and Mariette Yvinec},
  title     = {The {G}udhi Library: Simplicial Complexes and Persistent Homology},
  booktitle = {ICMS},
  year      = {2014},
}

@inproceedings{zigzag_reflection,
  author    = {Jean-Daniel Boissonnat and Cl\'ement Maria and Steve Oudot},
  title     = {Zigzag Persistent Homology Algorithm via Reflections},
  year      = {2014 $\ \ \ \ \ \ \ \ \ \ \ $ \emph{In Preparation}},
}

@misc{gudhi_stpcoh,
  author = {Cl\'ement Maria},
  title = "\textsc{Gudhi}, Simplex Tree and Persistent Cohomology Packages",
  note  = "\href{https://project.inria.fr/gudhi/software/}{\url{https://project.inria.fr/gudhi/software/}}"
}

%ARTICLES
%------------------------------------------------------------------
@article{boissonnatmariasimplextreealgorithmica,
year={2014},
issn={0178-4617},
journal={Algorithmica},
doi={10.1007/s00453-014-9887-3},
title={\href{http://dx.doi.org/10.1007/s00453-014-9887-3}{The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes}},
publisher={Springer US},
keywords={Simplicial complexes; Data structure; Computational topology; Flag complexes; Witness complexes},
author={Boissonnat, Jean-Daniel and Maria, Cl\'ement},
pages={1-22},
language={English}
}

@inproceedings{Garland,
 author = {Garland, Michael and Heckbert, Paul S.},
 title = {Surface simplification using quadric error metrics},
 booktitle = {Proceedings of the 24th annual conference on Computer graphics and interactive techniques},
 series = {SIGGRAPH '97},
 year = {1997},
 isbn = {0-89791-896-7},
 pages = {209--216},
 numpages = {8},
 publisher = {ACM Press/Addison-Wesley Publishing Co.},
 address = {New York, NY, USA},
 keywords = {level of detail, mutiresolution modeling, non-manifold, pair contraction, surface simplification},
} 


@inproceedings{Lindstrom,
 author = {Lindstrom, Peter and Turk, Greg},
 title = {Fast and Memory Efficient Polygonal Simplification},
 booktitle = {Proceedings of the Conference on Visualization '98},
 series = {VIS '98},
 year = {1998},
 isbn = {1-58113-106-2},
 location = {Research Triangle Park, North Carolina, USA},
 pages = {279--286},
 numpages = {8},
 publisher = {IEEE Computer Society Press},
 address = {Los Alamitos, CA, USA},
} 


@article{boissonnatmariacamalgorithmica,
journal={Submitted to Algorithmica},
title={The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology},
author={Jean-Daniel Boissonnat and Tamal K. Dey and Cl{\'e}ment Maria},
language={English},
}

@inproceedings{DBLP:conf/esa/BoissonnatDM13,
  author    = {Jean-Daniel Boissonnat and
               Tamal K. Dey and
               Cl{\'e}ment Maria},
  title     = {\href{http://dx.doi.org/10.1007/978-3-642-40450-4_59}{The Compressed Annotation Matrix: An Efficient Data Structure
               for Computing Persistent Cohomology}},
  booktitle = {ESA},
  year      = {2013},
  pages     = {695-706},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@inproceedings{boissonnatmariaesa2014,
  author    = {Jean-Daniel Boissonnat and
               Cl{\'e}ment Maria},
  title     = {Computing Persistent Homology with Various Coefficient Fields in a Single Pass},
  booktitle = {ESA},
  year      = {2014}
}

@inproceedings{DBLP:conf/esa/BoissonnatM12,
  author    = {Jean-Daniel Boissonnat and
               Cl{\'e}ment Maria},
  title     = {\href{http://dx.doi.org/10.1007/978-3-642-33090-2_63}{The Simplex Tree: An Efficient Data Structure for General
               Simplicial Complexes}},
  booktitle = {ESA},
  year      = {2012},
  pages     = {731-742},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}



%% hal-00922572, version 2
%% http://hal.inria.fr/hal-00922572
@techreport{boissonnat:hal-00922572,
    hal_id = {hal-00922572},
    url = {http://hal.inria.fr/hal-00922572},
    title = {\href{http://hal.inria.fr/hal-00922572}{Computing Persistent Homology with Various Coefficient Fields in a Single Pass}},
    author = {Boissonnat, Jean-Daniel and Maria, Cl{\'e}ment},
    abstract = {{In this article, we introduce the multi-field persistence diagram for the persistence homology of a filtered complex. It encodes compactly the superimposition of the persistence diagrams of the complex with several field coefficients, and provides a substantially more precise description of the topology of the filtered complex. Specifically, the multi-field persistence diagram encodes the Betti numbers of integral homology and the prime divisors of the torsion coefficients of the underlying shape. Moreover, it enjoys similar stability properties as the ones of standard persistence diagrams, with the appropriate notion of distance. These properties make the multi-field persistence diagram a useful tool in computational topology.}},
    keywords = {Computational Topology, Persistent homology, Modular reconstruction},
    language = {Anglais},
    affiliation = {GEOMETRICA - INRIA Sophia Antipolis / INRIA Saclay - Ile de France},
    pages = {19},
    type = {Rapport de recherche},
    institution = {INRIA},
    number = {RR-8436},
    year = {2013},
    month = Dec,
    pdf = {http://hal.inria.fr/hal-00922572/PDF/RR-8436.pdf},
}






@inproceedings{DBLP:conf/compgeom/CarlssonSM09,
  author    = {Gunnar E. Carlsson and
               Vin de Silva and
               Dmitriy Morozov},
  title     = {Zigzag persistent homology and real-valued functions},
  booktitle = {Symposium on Computational Geometry},
  year      = {2009},
  pages     = {247-256},
  ee        = {http://doi.acm.org/10.1145/1542362.1542408},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@inproceedings{DBLP:conf/compgeom/Cohen-SteinerEM06,
  author    = {David Cohen-Steiner and
               Herbert Edelsbrunner and
               Dmitriy Morozov},
  title     = {Vines and vineyards by updating persistence in linear time},
  booktitle = {Symposium on Computational Geometry},
  year      = {2006},
  pages     = {119-126},
  ee        = {http://doi.acm.org/10.1145/1137856.1137877},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@article{quiverrepresentations_derksenweyman,
  author  = {Harm Derksen and Jerzy Weyman},
  title   = {Quiver Representations},
  journal = {Notices of the AMS},
  volume  = {52},
  number  = {2},
  year    = {2005},
  pages   = {200-206}
}
@article{DBLP:journals/dcg/SilvaMV11,
  author    = {Vin de Silva and
               Dmitriy Morozov and
               Mikael Vejdemo-Johansson},
  title     = {Persistent Cohomology and Circular Coordinates},
  journal   = {Discrete {\&} Computational Geometry},
  volume    = {45},
  number    = {4},
  year      = {2011},
  pages     = {737-759},
  ee        = {http://dx.doi.org/10.1007/s00454-011-9344-x},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{RS62,
	author={J. B. Rosser and L. Schoenfeld},
	title={Approximate Formulas for some Functions of Prime Numbers},
	journal= ijm,
	volume= 6,
	year= 1962,
	pages={64-94},
	mrnumber={25 \#1139}
}
@article{DBLP:journals/siamcomp/Furer09,
  author    = {Martin F{\"u}rer},
  title     = {Faster Integer Multiplication},
  journal   = {SIAM J. Comput.},
  volume    = {39},
  number    = {3},
  year      = {2009},
  pages     = {979-1005},
  ee        = {http://dx.doi.org/10.1137/070711761},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{DBLP:journals/dcg/ZomorodianC05,
  author    = {Afra Zomorodian and
               Gunnar E. Carlsson},
  title     = {Computing Persistent Homology},
  journal   = {Discrete {\&} Computational Geometry},
  volume    = {33},
  number    = {2},
  year      = {2005},
  pages     = {249-274},
  ee        = {http://www.springerlink.com/index/10.1007/s00454-004-1146-y},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{DBLP:journals/dcg/Cohen-SteinerEH07,
  author    = {David Cohen-Steiner and
               Herbert Edelsbrunner and
               John Harer},
  title     = {Stability of Persistence Diagrams},
  journal   = {Discrete {\&} Computational Geometry},
  volume    = {37},
  number    = {1},
  year      = {2007},
  pages     = {103-120},
  ee        = {http://dx.doi.org/10.1007/s00454-006-1276-5},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{DBLP:journals/siamcomp/HafnerM91,
  author    = {James L. Hafner and
               Kevin S. McCurley},
  title     = {Asymptotically Fast Triangularization of Matrices Over Rings},
  journal   = {SIAM J. Comput.},
  volume    = {20},
  number    = {6},
  year      = {1991},
  pages     = {1068-1083},
  ee        = {http://dx.doi.org/10.1137/0220067},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{DBLP:journals/algorithmica/EfratIK01,
  author    = {Alon Efrat and
               Alon Itai and
               Matthew J. Katz},
  title     = {Geometry Helps in Bottleneck Matching and Related Problems},
  journal   = {Algorithmica},
  volume    = {31},
  number    = {1},
  year      = {2001},
  pages     = {1-28},
  ee        = {http://dx.doi.org/10.1007/s00453-001-0016-8},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{DBLP:journals/siamcomp/HopcroftK73,
  author    = {John E. Hopcroft and
               Richard M. Karp},
  title     = {An n$^{\mbox{5/2}}$ Algorithm for Maximum Matchings in Bipartite
               Graphs},
  journal   = {SIAM J. Comput.},
  volume    = {2},
  number    = {4},
  year      = {1973},
  pages     = {225-231},
  ee        = {http://dx.doi.org/10.1137/0202019},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

%------------------------------------------------------------------
@article{blockers2012,
  author    = {Dominique Attali and
               Andr{\'e} Lieutier and
               David Salinas},
  title     = {Efficient Data Structure for Representing and Simplifying
               Simplicial complexes in High Dimensions},
  journal   = {Int. J. Comput. Geometry Appl.},
  volume    = {22},
  number    = {4},
  year      = {2012},
  pages     = {279-304},
  ee        = {http://dx.doi.org/10.1142/S0218195912600060},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

%------------------------------------------------------------------
@article{rips2012,
    hal_id = {hal-00785072},
    url = {http://hal.archives-ouvertes.fr/hal-00785072},
    title = {{Vietoris-Rips Complexes also Provide Topologically Correct Reconstructions of Sampled Shapes}},
    author = {Attali, Dominique and Lieutier, Andr{\'e} and Salinas, David},
    keywords = {Shape reconstruction \sep Rips complexes \sep clique complexes \sep \v Cech complexes ; homotopy equivalence ; collapses ; high dimensions},
    language = {Anglais},
    affiliation = {Grenoble Images Parole Signal Automatique - GIPSA-lab , Laboratoire Jean Kuntzmann - LJK},
    pages = {448-465},
    journal = {Computational Geometry},
    volume = {46},
    number = {4, special issue },
    audience = {internationale },
    doi = {10.1016/j.comgeo.2012.02.009 },
    year = {2012},
    pdf = {http://hal.archives-ouvertes.fr/hal-00785072/PDF/2012-cgta-Rips.pdf},
}


%------------------------------------------------------------------
@article{DBLP:journals/corr/abs-1210-1429,
  author    = {Pawel Dlotko and
               Hubert Wagner},
  title     = {Computing homology and persistent homology using iterated
               Morse decomposition},
  journal   = {CoRR},
  volume    = {abs/1210.1429},
  year      = {2012},
  ee        = {http://arxiv.org/abs/1210.1429},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

%------------------------------------------------------------------
@article{tangentialcomplex2014,
author="Boissonnat, Jean-Daniel and Ghosh, Arijit",
title="Manifold Reconstruction Using Tangential Delaunay Complexes",
journal="Discrete {\&} Computational Geometry",
year="2014",
volume="51",
number="1",
pages="221--267",
abstract="We give a provably correct algorithm to reconstruct a k-dimensional smooth manifold embedded in d-dimensional Euclidean space. The input to our algorithm is a point sample coming from an unknown manifold. Our approach is based on two main ideas: the notion of tangential Delaunay complex defined in Boissonnat and Fl{\"o}totto (Comput. Aided Des. 36:161--174, 2004), Fl{\"o}totto (A coordinate system associated to a point cloud issued from a manifold: definition, properties and applications. Ph.D. thesis, 2003), Freedman (IEEE Trans. Pattern Anal. Mach. Intell. 24(10), 2002), and the technique of sliver removal by weighting the sample points (Cheng et al. in J. ACM 47:883--904, 2000). Differently from previous methods, we do not construct any subdivision of the d-dimensional ambient space. As a result, the running time of our algorithm depends only linearly on the extrinsic dimension d while it depends quadratically on the size of the input sample, and exponentially on the intrinsic dimension k. To the best of our knowledge, this is the first certified algorithm for manifold reconstruction whose complexity depends linearly on the ambient dimension. We also prove that for a dense enough sample the output of our algorithm is isotopic to the manifold and a close geometric approximation of the manifold.",
issn="1432-0444",
doi="10.1007/s00454-013-9557-2",
url="http://dx.doi.org/10.1007/s00454-013-9557-2"
}

%BOOKS
%------------------------------------------------------------------
@book{DBLP:tibkat_237559129,
   author              = {Saunders Mac Lane},
   title               = {Categories for the working mathematician},
   year                = {1998},
   ee                  = {http://www.zentralblatt-math.org/zmath/en/search/?an}
}


@book{Hatcher-algebraictopology2001,
    author = {Hatcher, Allen},
    day = {03},
    edition = {1},
    howpublished = {Paperback},
    isbn = {0521795400},
    keywords = {topology},
    month = dec,
    posted-at = {2008-06-25 09:53:39},
    priority = {2},
    publisher = {Cambridge University Press},
    title = {{Algebraic Topology}},
    url = {http://www.math.cornell.edu/\~{}hatcher/AT/AT.pdf},
    year = {2001}
}
@book{Munkres-elementsalgtop1984,
  author    = {James R. Munkres},
  title     = {Elements of algebraic topology},
  publisher = {Addison-Wesley},
  year      = {1984},
  isbn      = {978-0-201-04586-4},
  pages     = {I-IX, 1-454},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@book{DBLP:books/aw/Knuth81,
  author    = {Donald E. Knuth},
  title     = {The Art of Computer Programming, Volume II: Seminumerical
               Algorithms, 2nd Edition},
  publisher = {Addison-Wesley},
  year      = {1981},
  isbn      = {0-201-03822-6},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@book{DBLP:books/daglib/0025666,
  author    = {Herbert Edelsbrunner and
               John Harer},
  title     = {Computational Topology - an Introduction},
  publisher = {American Mathematical Society},
  year      = {2010},
  isbn      = {978-0-8218-4925-5},
  pages     = {I-XII, 1-241},
  ee        = {http://www.ams.org/bookstore-getitem/item=MBK-69},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@book{Gathen:2003:MCA:945759,
 author = {Gathen, Joachim Von Zur and Gerhard, Jurgen},
 title = {Modern Computer Algebra},
 year = {2003},
 isbn = {0521826462},
 edition = {2},
 publisher = {Cambridge University Press},
 address = {New York, NY, USA},
} 
@book{DBLP:books/aw/AhoHU74,
  author    = {Alfred V. Aho and
               John E. Hopcroft and
               Jeffrey D. Ullman},
  title     = {The Design and Analysis of Computer Algorithms},
  publisher = {Addison-Wesley},
  year      = {1974},
  isbn      = {0-201-00029-6},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
%------------------------------------------------------------------



%INPROCEEDINGS
%------------------------------------------------------------------

  crossref  = {DBLP:conf/esa/2013},

proceedings{DBLP:conf/esa/2013,
  editor    = {Hans L. Bodlaender and
               Giuseppe F. Italiano},
  title     = {Algorithms - ESA 2013 - 21st Annual European Symposium,
               Sophia Antipolis, France, September 2-4, 2013. Proceedings},
  booktitle = {ESA},
  publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {8125},
  year      = {2013},
  isbn      = {978-3-642-40449-8},
  ee        = {http://dx.doi.org/10.1007/978-3-642-40450-4},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@inproceedings{DBLP:conf/issac/StorjohannL96,
  author    = {Arne Storjohann and
               George Labahn},
  title     = {Asymptotically Fast Computation of {H}ermite Normal Forms
               of Integer Matrices},
  booktitle = {ISSAC},
  year      = {1996},
  pages     = {259-266},
  ee        = {http://doi.acm.org/10.1145/236869.237083},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}  crossref  = {DBLP:conf/issac/1996},
@inproceedings{DBLP:conf/issac/Storjohann96,
  author    = {Arne Storjohann},
  title     = {Near Optimal Algorithms for Computing Smith Normal Forms
               of Integer Matrices},
  booktitle = {ISSAC},
  year      = {1996},
  pages     = {267-274},
  ee        = {http://doi.acm.org/10.1145/236869.237084},

  bibsource = {DBLP, http://dblp.uni-trier.de}
}  crossref  = {DBLP:conf/issac/1996},
proceedings{DBLP:conf/issac/1996,
  editor    = {Erwin Engeler and
               B. F. Caviness and
               Yagati N. Lakshman},
  title     = {Proceedings of the 1996 International Symposium on Symbolic
               and Algebraic Computation, ISSAC '96, Zurich, Switzerland,
               July 24-26, 1996},
  booktitle = {ISSAC},
  publisher = {ACM},
  year      = {1996},
  isbn      = {0-89791-796-0},
  ee        = {http://dl.acm.org/citation.cfm?id=236869},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


proceedings{DBLP:conf/issac/1996,
  editor    = {Erwin Engeler and
               B. F. Caviness and
               Yagati N. Lakshman},
  title     = {Proceedings of the 1996 International Symposium on Symbolic
               and Algebraic Computation, ISSAC '96, Zurich, Switzerland,
               July 24-26, 1996},
  booktitle = {ISSAC},
  publisher = {ACM},
  year      = {1996},
  isbn      = {0-89791-796-0},
  ee        = {http://dl.acm.org/citation.cfm?id=236869},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


@inproceedings{socg_blockers_2011,
 author = {Attali, Dominique and Lieutier, Andr{\'e} and Salinas, David},
 title = {Efficient data structure for representing and simplifying simplicial complexes in high dimensions},
 booktitle = {Proceedings of the 27th annual ACM symposium on Computational geometry},
 series = {SoCG '11},
 year = {2011},
 location = {Paris, France},
 pages = {501--509},
 numpages = {9},
 keywords = {clique complexes, data structure, edge contraction, flag complexes, high dimensions, homotopy equivalence, shape reconstruction, shape simplification, simplicial complexes, vietoris-rips complexes},
} 



%------------------------------------------------------------------

%MISC
%------------------------------------------------------------------
@article{DBLP:journals/corr/abs-1208-5018,
  author    = {Tamal K. Dey and
               Fengtao Fan and
               Yusu Wang},
  title     = {Computing Topological Persistence for Simplicial Maps},
  journal   = {CoRR},
  volume    = {abs/1208.5018},
  year      = {2012},
  ee        = {http://arxiv.org/abs/1208.5018},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@article{DBLP:journals/corr/abs-1107-5665,
  author    = {Vin de Silva and
               Dmitriy Morozov and
               Mikael Vejdemo-Johansson},
  title     = {Dualities in persistent (co)homology},
  journal   = {CoRR},
  volume    = {abs/1107.5665},
  year      = {2011},
  ee        = {http://arxiv.org/abs/1107.5665},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

%------------------------------------------------------------------

%LIBRARY

%------------------------------------------------------------------
@misc{gmplib_cite,
title = "GMP, The GNU Multiple Precision Arithmetic Library",
note = "http://gmplib.org/",
}
%------------------------------------------------------------------




%TEMPORARY
%------------------------------------------------------------------
@inproceedings{deSilva:2013:GSP:2493132.2462402,
 author = {de Silva, Vin and Nanda, Vidit},
 title = {Geometry in the space of persistence modules},
 booktitle = {Proceedings of the twenty-ninth annual symposium on Computational geometry},
 series = {SoCG '13},
 year = {2013},
 isbn = {978-1-4503-2031-3},
 location = {Rio de Janeiro, Brazil},
 pages = {397--404},
 numpages = {8},
 url = {http://doi.acm.org/10.1145/2462356.2462402},
 doi = {10.1145/2462356.2462402},
 acmid = {2462402},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {discrete and computational geometry, embedding theorem, persistent homology},
} 
@article{Fredman:1984:SST:828.1884,
 author = {Fredman, Michael L. and Koml\'{o}s, J\'{a}nos and Szemer{\'e}di, Endre},
 title = {Storing a Sparse Table with {O}(1) Worst Case Access Time},
 journal = {J. ACM},
 issue_date = {July 1984},
 volume = {31},
 number = {3},
 month = jun,
 year = {1984},
 issn = {0004-5411},
 pages = {538--544},
 numpages = {7},
 url = {http://doi.acm.org/10.1145/828.1884},
 doi = {10.1145/828.1884},
 acmid = {1884},
 publisher = {ACM},
 address = {New York, NY, USA},
} 
%------------------------------------------------------------------



%%%%% TEMP
article{journals/moc/Moller08,
  added-at = {2011-04-10T00:00:00.000+0200},
  author = {M\"oller, Niels},
  biburl = {http://www.bibsonomy.org/bibtex/2a40c83ae0a723c978ff29ccaec7ff7ee/dblp},
  ee = {http://dx.doi.org/10.1090/S0025-5718-07-02017-0},
  interhash = {d2f425fef08e9b3ea347b12cbcf9792f},
  intrahash = {a40c83ae0a723c978ff29ccaec7ff7ee},
  journal = {Math. Comput.},
  keywords = {dblp},
  number = 261,
  pages = {589-607},
  timestamp = {2011-04-10T00:00:00.000+0200},
  title = {On Sch\"onhage's algorithm and subquadratic integer gcd computation.},
  url = {http://dblp.uni-trier.de/db/journals/moc/moc77.html#Moller08},
  volume = 77,
  year = 2008
}

@article{DBLP:journals/dcg/EdelsbrunnerLZ02,
  author    = {Herbert Edelsbrunner and
               David Letscher and
               Afra Zomorodian},
  title     = {Topological Persistence and Simplification},
  journal   = {Discrete Comput. Geom.},
  volume    = {28},
  number    = {4},
  year      = {2002},
  pages     = {511-533},
  ee        = {http://dx.doi.org/10.1007/s00454-002-2885-2},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}




inproceedings{DBLP:conf/esa/2012,
  editor    = {Leah Epstein and
               Paolo Ferragina},
  title     = {Algorithms - ESA 2012 - 20th Annual European Symposium,
               Ljubljana, Slovenia, September 10-12, 2012. Proceedings},
  booktitle = {ESA},
  publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {7501},
  year      = {2012},
  isbn      = {978-3-642-33089-6},
  ee        = {http://dx.doi.org/10.1007/978-3-642-33090-2},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}



@article{SMV11,
  author    = {V. de Silva and
               D. Morozov and
               M. Vejdemo-Johansson},
  title     = {Persistent cohomology and circular coordinates},
  journal   = {Discrete Comput. Geom.},
  volume    = {45},
  pages = {737-759},
  year      = {2011},
}
@article{SMV211,
  author    = {V. de Silva and
               D. Morozov and
               M. Vejdemo-Johansson},
  title     = {Dualities in persistent (co)homology},
  journal   = {Inverse Problems},
  volume    = {27},
  year      = {2011},
  pages     = {124003},
}





inproceedings{DBLP:conf/soda/BentleyS97,
  author    = {Jon Louis Bentley and
               Robert Sedgewick},
  title     = {Fast Algorithms for Sorting and Searching Strings},
  booktitle = {SODA},
  year      = {1997},
  pages     = {360-369},
  ee        = {http://doi.acm.org/10.1145/314161.314321},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@inproceedings{CO08,
  author    = {F. Chazal and S. Oudot},
  title     = {Towards persistence-based reconstruction in Euclidean spaces},
  booktitle   = {Proc. 24th. Annu. Sympos. Comput. Geom.},
  year      = {2008},
  pages = {231-241}
}
inproceedings{DBLP:conf/soda/1997,
  editor    = {Michael E. Saks},
  title     = {Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete
               Algorithms, 5-7 January 1997, New Orleans, Louisiana},
  booktitle = {SODA},
  publisher = {ACM/SIAM},
  year      = {1997},
  isbn      = {0-89871-390-0},
  ee        = {http://dl.acm.org/citation.cfm?id=314161},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}




@inproceedings{attali-rips_approx,
  author    = {Dominique Attali and
               Andr{\'e} Lieutier and
               David Salinas},
  title     = {Vietoris-rips complexes also provide topologically correct
               reconstructions of sampled shapes},
  booktitle = {Symposium on Computational Geometry},
  year      = {2011},
  pages     = {491-500},
  ee        = {http://doi.acm.org/10.1145/1998196.1998276},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}






@article{Carlsson:2008:LBS:1325290.1325300,
 author = {Carlsson, Gunnar and Ishkhanov, Tigran and Silva, Vin and Zomorodian, Afra},
 title = {On the Local Behavior of Spaces of Natural Images},
 journal = {Int. J. Comput. Vision},
 volume = {76},
 issue = {1},
 month = {January},
 year = {2008},
 issn = {0920-5691},
 pages = {1--12},
 numpages = {12},
 url = {http://portal.acm.org/citation.cfm?id=1325290.1325300},
 doi = {10.1007/s11263-007-0056-x},
 acmid = {1325300},
 publisher = {Kluwer Academic Publishers},
 address = {Hingham, MA, USA},
 keywords = {Filtration, Klein bottle, Manifold, Natural images, Persistent homology, Topology},
} 

article{DBLP:journals/ijcv/LeePM03,
  author    = {Ann B. Lee and
               Kim Steenstrup Pedersen and
               David Mumford},
  title     = {The Nonlinear Statistics of High-Contrast Patches in Natural
               Images},
  journal   = {International Journal of Computer Vision},
  volume    = {54},
  number    = {1-3},
  year      = {2003},
  pages     = {83-103},
  ee        = {http://dx.doi.org/10.1023/A:1023705401078},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


@article{martin2010top,
title={Topology of cyclo-octane energy landscape.},
author={Martin, S. and Thompson, A. and Coutsias, E.A. and Watson, J.},
journal={J Chem Phys},
volume={132},
number={23},
pages={234115},
year={2010},
abstract={Understanding energy landscapes is a major challenge in chemistry and biology. Although a wide variety of methods have been invented and applied to this problem, very little is understood about the actual mathematical structures underlying such landscapes. Perhaps the most general assumption is the idea that energy landscapes are low-dimensional manifolds embedded in high-dimensional Euclidean space. While this is a very mild assumption, we have discovered an example of an energy landscape which is nonmanifold, demonstrating previously unknown mathematical complexity. The example occurs in the energy landscape of cyclo-octane, which was found to have the structure of a reducible algebraic variety, composed of the union of a sphere and a Klein bottle, intersecting in two rings.}
}
 

book{hatcher2002algebraic,
  title={Algebraic Topology},
  author={Hatcher, A.},
  isbn={9780521795401},
  lccn={00065166},
  url={http://books.google.fr/books?id=BjKs86kosqgC},
  year={2002},
  publisher={Cambridge University Press}
}



@article{DBLP:journals/cagd/DelfinadoE95,
  author    = {Cecil Jose A. Delfinado and
               Herbert Edelsbrunner},
  title     = {An incremental algorithm for {B}etti numbers of simplicial
               complexes on the 3-sphere},
  journal   = {Computer Aided Geometric Design},
  volume    = {12},
  number    = {7},
  year      = {1995},
  pages     = {771-784},
  ee        = {http://dx.doi.org/10.1016/0167-8396(95)00016-Y},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


@book{Cormen:2001:IA:580470,
 author = {Cormen, Thomas H. and Stein, Clifford and Rivest, Ronald L. and Leiserson, Charles E.},
 title = {Introduction to Algorithms},
 year = {2001},
 isbn = {0070131511},
 edition = {2nd},
 publisher = {McGraw-Hill Higher Education},
} 

@article{DBLP:journals/focm/CarlssonS10,
  author    = {Gunnar E. Carlsson and
               Vin de Silva},
  title     = {Zigzag Persistence},
  journal   = {Foundations of Computational Mathematics},
  volume    = {10},
  number    = {4},
  year      = {2010},
  pages     = {367-405},
  ee        = {http://dx.doi.org/10.1007/s10208-010-9066-0},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@article{ghrist_coverage,
  author    = {V. de Silva and R. Ghrist},
  title     = {Coverage in sensor network via persistent homology},
  journal   = {Algebraic {\&} Geometric Topology},
  volume    = {7},
  year      = {2007},
  pages     = {339-358},
}
@article{mischaikow_nanda_morse,
year={2013},
issn={0179-5376},
journal={Discrete {\&} Computational Geometry},
volume={50},
number={2},
doi={10.1007/s00454-013-9529-6},
title={Morse Theory for Filtrations and Efficient Computation of Persistent Homology},
url={http://dx.doi.org/10.1007/s00454-013-9529-6},
publisher={Springer US},
keywords={Computational topology; Discrete Morse theory; Persistent homology},
author={Mischaikow, Konstantin and Nanda, Vidit},
pages={330-353},
language={English}
}


@inproceedings{DBLP:conf/compgeom/MilosavljevicMS11,
  author    = {Nikola Milosavljevic and
               Dmitriy Morozov and
               Primoz Skraba},
  title     = {Zigzag persistent homology in matrix multiplication time},
  booktitle = {Symposium on Comp. Geom.},
  year      = {2011},
  ee        = {http://doi.acm.org/10.1145/1998196.1998229},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
proceedings{DBLP:conf/compgeom/2011,
  editor    = {Ferran Hurtado and
               Marc J. van Kreveld},
  title     = {Proceedings of the 27th ACM Symposium on Computational Geometry,
               Paris, France, June 13-15, 2011},
  booktitle = {Symposium on Computational Geometry},
  publisher = {ACM},
  year      = {2011},
  isbn      = {978-1-4503-0682-9},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@article{DBLP:journals/comgeo/ChenK13,
  author    = {Chao Chen and
               Michael Kerber},
  title     = {An output-sensitive algorithm for persistent homology},
  journal   = {Comput. Geom.},
  volume    = {46},
  number    = {4},
  year      = {2013},
  pages     = {435-447},
  ee        = {http://dx.doi.org/10.1016/j.comgeo.2012.02.010},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


@incollection{Bauer:arXiv1303.0477,
year={2014},
isbn={978-3-319-04098-1},
booktitle={Topological Methods in Data Analysis and Visualization III},
doi={10.1007/978-3-319-04099-8_7},
title={Clear and Compress: Computing Persistent Homology in Chunks},
url={http://dx.doi.org/10.1007/978-3-319-04099-8_7},
author={Bauer, Ulrich and Kerber, Michael and Reininghaus, Jan},
pages={103-117},
language={English}
}
@inproceedings{DBLP:conf/alenex/BauerKR14,
  author    = {Ulrich Bauer and
               Michael Kerber and
               Jan Reininghaus},
  title     = {Distributed Computation of Persistent Homology},
  booktitle = {ALENEX},
  year      = {2014},
  pages     = {31-38},
  ee        = {http://dx.doi.org/10.1137/1.9781611973198.4},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
@inproceedings{DBLP:conf/compgeom/DeyFW14,
  author    = {Tamal K. Dey and
               Fengtao Fan and
               Yusu Wang},
  title     = {Computing Topological Persistence for Simplicial Maps},
  booktitle = {Symposium on Computational Geometry},
  year      = {2014},
  pages     = {345},
  ee        = {http://doi.acm.org/10.1145/2582112.2582165},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@INPROCEEDINGS{Chen11persistenthomology,
    author = {Chao Chen and Michael Kerber},
    title = {Persistent homology computation with a twist},
    booktitle = {Proceedings 27th European Workshop on Computational Geometry},
    year = {2011}
}


@ARTICLE{Morozov05persistencealgorithm,
    author = {Dmitriy Morozov},
    title = {Persistence algorithm takes cubic time in worst case},
    journal = {BioGeometry News, Dept. Comput. Sci., Duke Univ},
    year = {2005}
}

@article{DBLP:journals/corr/abs-1205-3669,
  author    = {Peter Bubenik and
               Jonathan A. Scott},
  title     = {Categorification of persistent homology},
  journal   = {CoRR},
  volume    = {abs/1205.3669},
  year      = {2012},
  ee        = {http://arxiv.org/abs/1205.3669},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

misc{buddha_stanford_scan,
 author = "",
   title = "The Stanford 3D Scanning Repository",
    note  = "http://graphics.stanford.edu/data/3Dscanrep/"
}
@misc{dionysus_morozov,
 author = "Dmitriy Morozov",
   title = "\textsc{Dionysus}",
    note  = "http://www.mrzv.org/software/dionysus/"
}

@misc{phat_lib,
author={Bauer, Ulrich and Kerber, Michael and Reininghaus, Jan},
   title = "\textsc{Phat}",
    note  = "https://code.google.com/p/phat/"
}

misc{ann_mount,
author = "David M. Mount
and Sunil Arya",
    title = "\textsc{ANN}, {A}pproximate {N}earest {N}eighbors {L}ibrary",
    note  = "http://www.cs.sunysb.edu/~algorith/implement/ANN/implement.shtml"
}

misc{jplex_cite,
  author    = "Sexton, Harlan and Johansson, Mikael Vejdemo",
  title     = "\textsc{JPlex}",
  year      = "2009",
  note = "http://comptop.stanford.edu/programs/jplex/"
}

@book{kaczynski2004computational,
  title={Computational Homology},
  author={Kaczynski, T. and Mischaikow, K. and Mrozek, M.},
  isbn={9780387408538},
  lccn={03061109},
  series={Applied Mathematical Sciences},
  url={https://books.google.fr/books?id=AShKtpi3GecC},
  year={2004},
  publisher={Springer New York}
}

@ARTICLE{peikert2012topological,
year={2012},
isbn={978-3-642-23174-2},
booktitle={Topological Methods in Data Analysis and Visualization II},
series={Mathematics and Visualization},
editor={Peikert, Ronald and Hauser, Helwig and Carr, Hamish and Fuchs, Raphael},
doi={10.1007/978-3-642-23175-9_7},
title={Efficient Computation of Persistent Homology for Cubical Data},
url={http://dx.doi.org/10.1007/978-3-642-23175-9_7},
publisher={Springer Berlin Heidelberg},
author={Wagner, Hubert and Chen, Chao and Vucini, Erald},
pages={91-106},
language={English}
}