In this paper we present a methodology to develop efficient and deadlock free routing algorithms for Network-on-Chip (NoC) platforms which are specialized for an application or a set of concurrent applications. The proposed methodology, called Application Specific Routing Algorithm (APSRA), exploits the application specific information regarding pairs of cores which communicate and other pairs which never communicate in the NoC platform to maximize communication adaptivity and performance. The methodology also exploits the known information regarding concurrency/non-concurrency of communication transactions among cores for the same purpose. We demonstrate, through analysis of adaptivity as well as simulation based evaluation of latency and throughput, that algorithms produced by the proposed methodology give significantly higher performance as compared to other deadlock free algorithms for both homogeneous as well as heterogeneous 2D mesh topology NoC systems. For example, for homogeneous mesh NoC, APSRA results in approximately 30% less average delay as compared to Odd-Even algorithm just below saturation load. Similarly the saturation load point for APSRA is significantly higher as compared to other adaptive routing algorithms for both homogeneous and non-homogeneous mesh networks.