Minimum spanning tree (MST) based clustering algorithms have been employed successfully to detect clusters of heterogeneous nature. Given a dataset of n random points, most of the MST-based clustering algorithms first generate a complete graph G of the dataset and then construct MST from G. The first step of the algorithm is the major bottleneck which takes O(n 2) time. This paper proposes two algorithms namely MST-based clustering on K-means Graph and MST-based clustering on Bi-means Graph for reducing the computational overhead. The proposed algorithms make use of a centroid based nearest neighbor rule to generate a partition-based Local Neighborhood Graph (LNG). We prove that both the size and the computational time to construct the graph (LNG) is O(n 3/2), which is a \(O(\sqrt n)\) factor improvement over the traditional algorithms. The approximate MST is constructed from LNG in \(O(n^{3/2} \lg n)\) time, which is asymptotically faster than O(n 2). The advantage of the proposed algorithms is that they do not require any parameter setting which is a major issue in many of the nearest neighbor finding algorithms. Experimental results demonstrate that the computational time has been reduced significantly by maintaining the quality of the clusters obtained from the MST.