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A new architecture for network on chip (NOC) called Mesh-Tree and its deterministic algorithm has been presented. In this paper, we present an adaptive deadlock-free router. A Mesh-Tree is a multilayered, 3D, pyramidal architecture. Each layer is a mesh and trees are used to connect adjacent layers. This architecture is good for broadcasting and high speed communications. The simulation results show that the adaptive deadlock-free routing algorithm has a higher performance/cost ratio than the deterministic algorithm and the West-first algorithm used in the mesh architecture.