Table III.

Summary of the Complexity of Each Step of the ASAP Algorithm.

Stage	Complexity	# of calls
Break 1-hop neighborhood into patches	O(k + m’)	n
Patch embedding by SMACOF	O(k3 + k3/2t)	N
Patch embedding by FULL-SDP	O(k2m’2.5 + m’3.5)	N
Patch intersection	O(k)	M
Patch alignment	O(k)	M
Top eigenvector computation	O(Mζ)	2
Linear least squares	$O\left(m\sqrt{\kappa }\right)$	2
Total	$O\left(npoly\right(\mathcal{k},m^{\prime },t,\zeta )+m\sqrt{\kappa })$

t denotes the number of iterations of the SMACOF algorithm, ζ the number of iterations of the power method, and κ the condition number of the matrix T^T T (where T is the least squares matrix from Step 3).