TL;DR
This paper demonstrates that Betti numbers, which are topological invariants of simplicial complexes with bounded degrees, can be efficiently tested in constant time, enabling quick topological analysis.
Contribution
It introduces a method to test Betti numbers of bounded-degree simplicial complexes in constant time, a novel approach in topological data analysis.
Findings
Betti numbers are testable in constant time for bounded-degree complexes.
The method applies to simplicial complexes with bounded vertex degrees.
This enables efficient topological property testing.
Abstract
We prove that the Betti numbers of simplicial complexes of bounded vertex degrees are testable in constant time.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · History and advancements in chemistry