The general problem of quantizing observation signals appears in different aspects of data processing from special code designs to realization of low-complexity receivers. To this end, a new framework, known as information bottleneck method, has recently attracted a great deal of attention. In this paper, after introducing this framework and providing the Iterative Information Bottleneck algorithm as the primary pertinent solution, we also discuss three other heuristics aiming to solve the similar problem efficiently. Since the resultant solution of considered approaches is locally optimum, it strongly depends on the choice of initialization. The main contribution of this work is to prove the equivalence of these algorithms asymptotically, i.e., assuming an infinite run of algorithms for the extreme case of infinitely large trade-off parameter. We also substantiate this claim by means of computer-based simulations.