All the four operations (i.e. three matrix multiplications and one matrix inversion) contribute a complexity of \(O\left(m^{3}\right)\). The other algorithm that is IDV [18], adopts a two-dimensional hyperbolic method for location estimation. The significant operations for complexity analysis of the two-dimensional hyperbolic method are matrix multiplication and matrix inversion. It (i.e. two-dimensional hyperbolic method) needs matrix multiplication and matrix inversion three times and one time respectively also. Therefore the computational complexity of IDV [18] for the last step to localize is also same as that of DV-Hop algorithm that is \(O\left(m^{3}\right)\). Here it is worthwhile to consider that IDV [18] contributes one more cost component of \(O\left(m^{2}\right)\) by each anchor, node to calculate the hop size correction factor. In IDV [18], since each anchor node corrects its hop size by \(O\left(m^{2}\right)\) therefore the net complexity of correction factor becomes \(O\left(m^{3}\right)\) for the whole network. The proposed algorithm ODR is dependent upon linear programming in its last step, which contributes\(O\left(m^{3.5}\right)\) as suggested by Karmarkar [7]. The optimized solution of a linear programming problem is also dependent upon the number of constraints \((Con)\). It implies that based on constraints the computational complexity of proposed ODR is \(O(Con)\)[5, 3] where \(Con\leq m\).