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A routing algorithm defines a route which packet traverses to get to destination. In this research we study some kind of routing algorithms that are used in internal connections networks of multi-processor and multi-computers systems. Then we discuss about some routing algorithms which have been implemented network on chip architecture. First, we present a group of routing algorithms based on various criterions, and review so-called category. Afterwards, we study adaptive and deterministic routing algorithms and express circular model applying in internal connections networks and its governing rules in order to prevent dead lock. Then we survey adaptive algorithms such as deflection routing, odd-even, negative-first, north-last, west-first and finally we study and review routing algorithms like backtracking protocols, and deflection routing.