Using Membrane Computing for Effective Homology |
| |
Authors: | Daniel Díaz-Pernil Hepzibah A Christinal Miguel A Gutiérrez-Naranjo Pedro Real |
| |
Affiliation: | 1. Research Group on Computational Topology and Applied Mathematics, Universidad de Sevilla, Sevilla, Spain 2. Karunya University, Coimbatore, Tamilnadu, India 3. Research Group on Natural Computing, Universidad de Sevilla, Sevilla, Spain
|
| |
Abstract: | Effective Homology is an algebraic-topological method based on the computational concept of chain homotopy equivalence on a cell complex. Using this algebraic data structure, Effective Homology gives answers to some important computability problems in Algebraic Topology. In a discrete context, Effective Homology can be seen as a combinatorial layer given by a forest graph structure spanning every cell of the complex. In this paper, by taking as input a pixel-based 2D binary object, we present a logarithmic-time uniform solution for describing a chain homotopy operator $\phi $ for its adjacency graph. This solution is based on Membrane Computing techniques applied to the spanning forest problem and it can be easily extended to higher dimensions. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|