This paper proposes a novel common subgraph extraction algorithm which aims to minimize the total number of gates (reconfiguration area overhead) involved in implementing compute-intensive scientific and media applications using reconfigurable architectures. Motivation behind the proposed research is illustrated using an example from Biochemical Algorithms Library (BALL). The design of novel context adaptable architectures to implement common subgraphs is also proposed with an example from the video warping functions of the MPEG-4 standard. Three different models of mapping such architectures onto hybrid/pure FPGA systems are proposed. Estimates obtained by applying these techniques and architectures for various media and scientific functions are shown.