In this paper, we study the CCD(Clustering with Circular Distance) and the COD(Clustering with Obstructed Distance) problems to be considered when objects are being clustered in a circularly search space and a search space with the presence of obstacles. We also propose a now clustering algorithm for clustering efficiently objects that the insertion or the deletion is occurring frequently in multi-dimensional search space. The distance function for solving the CCD and COD Problems is defined in the Proposed clustering algorithm. This algorithm is included a clustering method to create clusters that have a high spatial locality by minimum computation time.