Abstract: In a massively parallel processors（MPP） system, the routing algorithm constitutes the primary factor influencing the performance of the interconnect network and MPP system. Through careful analysis of message routing on interconnection network, the concept of “the Best Network for Routing（BNR）” is proposed. Using BNR, a framework for designing a new minimal deadlock free fully adaptive algorithm（ MDF\+2A \+2） is described, and a kind of BNR based MDF\+2A \+2s on Mesh: BBFAM is proved in this paper. The analysis shows that they are the high performance fully adaptive algorithms, so the BNR framework can give good guidelines to the interconnection network designers.