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Searching combinatorial optimality using graph-based homology information

Opened Access Searching combinatorial optimality using graph-based homology information


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Autor: Real Jurado, Pedro
Molina Abril, Helena
González Lorenzo, Aldo
Bac, Alexandra
Mari, Jean-Luc
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Fecha: 2015
Publicado en: Applicable Algebra in Engineering, Communication and Computing, 26 (1), 103-120.
Tipo de documento: Artículo
Resumen: This paper analyses the topological information of a digital object O under a combined combinatorial-algebraic point of view. Working with a topology-preserving cellularization K(O) of the object, algebraic and combinatorial tools are jointly used. The combinatorial entities used here are vector fields, V-paths and directed graphs. In the algebraic side, chain complexes with extra 2-nilpotent operators are considered. By mixing these two perspectives we are able to explore the problems of combinatorial and homological optimality. Combinatorial optimality is understood here as the problem for constructing a discrete gradient vector field (DGVF) in the sense of Discrete Morse Theory, such that it has the least possible number of critical cells. Fixing Z/2Z as field of coefficients, by homological ‘optimality’ we mean the problem of constructing a 2-nilpotent codifferential map ϕ:C∗(K(O))→C∗+1(K(O)) for finite linear combinations of cells in K(O), called homology integral operator. The h...
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