/*    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_