Information Centric Network (ICN) is one of the growing network environments that provides the majority of internet activities, which are related to information access and delivery. In ICN, users can obtain information contents of the caches in ICN routers. However, how to use the caches effectively is one of the main challenges faced by the researchers. Thus, several research studies are developed for reducing the cache overlaps among routers, since that limits the interests towards the caches. In order to address this problem, a new shortest path estimation algorithm (Modified Floyd Warshall Algorithm (MFWA)) was developed to identify the shortest path in each subnet for retrieving the cache memory data quickly. In MFWA, a new iterative matrix was used to eliminate the invalid paths that helps to retrieve the cache memory data quickly. In this research work, an ICN network was generated based on the concept of GEANT topology and tested with dissimilar cache management policies such as Hash Routing Symmetric (HR-SYMM), Hash Routing Asymmetric (HR-ASYMM), Hash Routing Hybrid Asymmetric Multicast (HR-HYBRID-AM), Hash Routing Hybrid Symmetric Multicast (HR-HYBRID-SM), and Hash Routing Multicast (HR-MULTICAST). In experimental section, the proposed shortest path estimation method showed better performance in light of latency, link load and cache hit ratio as compared to the existing approaches: Floyd Warshall Algorithm (FWA), Dijkstra's Algorithm (DA), and Enhanced Dijkstra's Algorithm (EDA). The experimental outcome showed that the proposed approach improved cache hit ratio up to 4-30% as related to the existing methods.