An improved algorithm for Generalized Čech complex construction
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In this paper, we present an algorithm that computes the generalized Čech complex for a finite set of disks where each may have a different radius in 2D space. An extension of this algorithm is also proposed for a set of balls in 3D space with different radius. To compute a k-simplex, we leverage the computation performed in the round of (k-1)-simplices such that we can reduce the number of potential candidates to verify to improve the efficiency. An efficient verification method is proposed to confirm if a k-simplex can be constructed on the basis of the (k-1)-simplices. We demonstrate the performance with a comparison to some closely related algorithms.
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