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diff --git a/src/Toplex_map/doc/Intro_Toplex_map.h b/src/Toplex_map/doc/Intro_Toplex_map.h new file mode 100644 index 00000000..a925dc2b --- /dev/null +++ b/src/Toplex_map/doc/Intro_Toplex_map.h @@ -0,0 +1,61 @@ +/* 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 + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#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_ |