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/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author: François Godi, Vincent Rouvreau
*
* Copyright (C) 2017 INRIA
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#ifndef DOC_TOPLEX_MAP_INTRO_TOPLEX_MAP_H_
#define DOC_TOPLEX_MAP_INTRO_TOPLEX_MAP_H_
// needs namespace for Doxygen to link on classes
namespace Gudhi {
/** \defgroup toplex_map Toplex Map
*
* \author François Godi
* @{
*
* \section toplexmapdefinition Definition
*
* A Toplex_map is a data structure to represent and store a simplicial complex. A "toplex" is the contraction of
* "top-simplex", also known as a maximal simplex. The plural form of "toplex" will be called "toplices".
*
* Let's consider a simplicial complex, denote by \f$d\f$ its dimension and by \f$k\f$ its number of maximal simplices.
* Furthermore, denote by \f$\Gamma_0\f$ the maximal number of toplices, i.e. maximal simplices, that contain a same
* vertex.
*
* The goal of the Toplex Map is both to represent the complex in optimal O(kd) space and to provide fast standard
* operations such as : insertion, removal, contraction of an edge, collapses and membership of a simplex. The time
* needed for these operation is linear or quadratic in \f$\Gamma_0\f$ and \f$d\f$.
*
* Toplex map is composed firstly of a raw storage of toplices and secondly of a map which associate any vertex to a
* set of pointers toward all toplices containing this vertex. The data structure is described in
* \cite boissonnat_et_al:LIPIcs:2015:5098 (aka. Simplex Array List or SAL).
*
* \image html map.png
*
* The performances are a lot better than the `Simplex_tree` as soon you use maximal simplices and not simplices
* (cf. \cite DBLP:journals/corr/BoissonnatS16 ).
*
*/
/** @} */ // end defgroup toplex_map
} // namespace Gudhi
#endif // DOC_TOPLEX_MAP_INTRO_TOPLEX_MAP_H_
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