Nearly all bitrate adaptive video content delivered today is streamed using protocols that run a purely client based adaptation logic. The resulting lack of coordination may lead to suboptimal user experience and resource utilization. As a response, approaches that include the network and servers in the adaptation process are emerging. In this article, we present an optimized solution for network assisted adaptation specifically targeted to mobile streaming in multi-access edge computing (MEC) environments. Due to NP-Hardness of the problem, we have designed a heuristic-based algorithm with minimum need for parameter tuning and having relatively low complexity. We then study the performance of this solution against two popular client-based solutions, namely Buffer-Based Adaptation (BBA) and Rate-Based Adaptation (RBA), as well as to another network assisted solution. Our objective is two fold: First, we want to demonstrate the efficiency of our solution and second to quantify the benefits of network-assisted adaptation over the client-based approaches in mobile edge computing scenarios. The results from our simulations reveal that the network assisted adaptation clearly outperforms the purely client-based DASH heuristics in some of the metrics, not all of them, particularly, in situations when the achievable throughput is moderately high or the link quality of the mobile clients does not differ from each other substantially.