In this paper, we characterize minimal elements in a finite \(T_{0}\) space under the specialization order based on its incidence matrix. Moreover, we give a new algorithm to compute the covering dimension of a finite \(T_{0}\) space by finding minimal elements under the specialization order. As its time complexity is O(n), the algorithm is fast for \(T_0\) spaces. Finally, since a topological space and its Kolmogorov quotient space have the same covering dimension, we can compute the covering dimension for every finite topological space on the basis of the above algorithm. Extensive experiments are also carried out on 7 artificial data sets demonstrating the effectiveness of our proposed algorithms.
