In the context of noisy source coding, contrary to the conventional Rate-Distortion theory, the so-called Information Bottleneck method formulates the existent fundamental complexity-precision trade-off in a symmetric and purely information-theoretic fashion. Since the pertinent optimization task to design the quantizer is quite demanding, a number of heuristics have been developed to provide practically feasible procedures at the expense of yielding suboptimal solutions. In this paper, we consider two pertinent routines originally appeared in totally different applications and set out to precisely prove their algorithmic equivalence by conducting a thorough analysis over the corresponding algorithmic steps. We further corroborate our theoretical investigation employing computer-based simulations.