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 \(Con\leq m\).