Abstract
Effective Homology is an algebraic-topological method based on the com- putational concept of chain homotopy equivalence on a cell complex. Using this algebraic data structure, Effective Homology gives answers to some important com- putability 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 cellofthecomplex.Inthispaper,bytakingasinputapixel-based2Dbinaryobject,we present a logarithmic-time uniform solution for describing a chain homotopy operator φ for its adjacency graph. This solution is based on Membrane Computing tech- niques applied to the spanning forest problem and it can be easily extended to higher dimensions.
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