Edge computing is a distributed computing paradigm that brings computation and data storage closer to the user's geographical location to improve response times and save bandwidth. It also helps to power a variety of applications requiring low latency. These application data hosted on the cloud needs to be transferred to the respective edge servers in a specific area to help provide low-latency app functionalities to the users of that area. Meanwhile, these arbitrary heavy data transactions from the cloud to the edge servers result in high cost and time penalties. Thus, we need an application data distribution strategy that minimizes these penalties within the app vendors' specific latency constraint. In this work, we provide a refined formulation of an optimal approach to solve this Edge Data Distribution (EDD) problem using Integer Programming (IP) technique. Due to the time complexity limitation of the IP approach, we suggest an O(k) approximation algorithm based on network Steiner tree estimation (EDD-NSTE) for estimating solutions to dense, large-scale EDD problems. Integer Programming and EDD-NSTE are evaluated on a standard real-world EUA data set and the result demonstrates that EDD-NSTE significantly outperforms with a performance margin of 86.67% over the other three representative approaches and the state-of-the-art approach.