As the problem of GOSST building belongs to NP compete domain, heuristics for the problem ask for immense amount execution time and computations in large scale inputs. In this paper, we propose an efficient mechanism for GOSST construction using space locality PTAS. For 40,000 input nodes with maximum weight 100, the proposed space locality PTAS GOSST with 16 unit areas can reduce about 4.00% of connection cost and 89.26% of execution time less than weighted minimum spanning tree method. Though the proposed method increases 0.03% of connection cost more, but cuts down 96.39% of execution time less than approximate GOSST method (SGOSST) without PTAS. Therefore the proposed space locality PTAS GOSST mechanism can work moderately well to many useful applications where a greate number of weighted inputs should be connected in short time with approximate minimum connection cost.