Integer coefficient selection is an important decoding
step in the implementation of compute-and-forward (C-F)
relaying scheme. Choosing the optimal integer coefficients in CF
has been shown to be a shortest vector problem (SVP) which
is known to be NP hard in its general form. Exhaustive search
of the integer coefficients is only feasible in complexity for small
number of users while approximation algorithms such as LenstraLenstra-Lovasz
(LLL) lattice reduction algorithm only find a
vector within an exponential factor of the shortest vector. An
optimal deterministic algorithm was proposed for C-F by Sahraei
and Gastpar specifically for the real valued channel case. In this
paper, we adapt their idea to the complex valued channel and
propose an efficient search algorithm to find the optimal integer
coefficient vectors over the ring of Gaussian integers and the ring
of Eisenstein integers. A second algorithm is then proposed that
generalises our search algorithm to the Integer-Forcing MIMO CF
receiver. Performance and efficiency of the proposed algorithms
are evaluated through simulations and theoretical analysis.