  In this paper, we present an algorithm that computes the generalized \v{C}ech
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.
