Packet classification is crucial for the Internet to provide more value-added services and guaranteed quality of service. Besides hardware-based solutions, many software-based classification algorithms have been proposed. However, classifying at 10Gbps speed or higher is a challenging problem and it is still one of the performance bottlenecks in core routers. In general, classification algorithms face the same challenge of balancing between high classification speed and low memory requirements. This paper proposes a modified Recursive Flow Classification (RFC) algorithm, Bitmap-RFC, which significantly reduces the memory requirements of RFC by applying a bitmap compression technique. To speed up classifying speed, we experiment on exploiting the architectural features of a many-core and multithreaded architecture from algorithm design to algorithm implementation. As a result, Bitmap-RFC strikes a good balance between speed and space. It can not only keep high classification speed but ...