Efficient Computation of the Large Inductive Dimension Using Order- and Graph-theoretic Means

DOI10.3233/FI-2020-1981zbMath1504.54025OpenAlexW3115014921MaRDI QIDQ4988918

Michael Winter, Henning Schnoor, Rudolf Berghammer

Publication date: 20 May 2021

Published in: Fundamenta Informaticae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/fi-2020-1981

zbMATH Keywords

finite topological spacelarge inductive dimensionlinear directed binary treespecialization pre-order

Mathematics Subject Classification ID

Partial orders, general (06A06) Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) Dimension theory in general topology (54F45) Applications of general topology to computer science (e.g., digital topology, image processing) (54H30) Computational aspects of digital topology (68U03)

Uses Software

• RelView

Cites Work

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• Covering dimension and finite spaces
• Finite spaces: a reduction algorithm for the computation of the small inductive dimension
• A strong-connectivity algorithm and its applications in data flow analysis
• An algorithm of polynomial order for computing the covering dimension of a finite space
• Order- and graph-theoretic investigation of dimensions of finite topological spaces and Alexandroff spaces
• A computing procedure for the small inductive dimension of a finite \(\mathrm{T}_0\)-space
• Topological dimension and dynamical systems. Translated from the French by the author
• Small inductive dimension and Alexandroff topological spaces
• Topological sorting of large networks
• Computer Algebra in Scientific Computing
• Finite Topological Spaces
• Depth-First Search and Linear Graph Algorithms

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