### The Reliability Evaluation of Cube Based Interconnection Networks Under Node Failure Model

#### Abstract

Under node failure model, a cube may operate in a gracefully degradable manner by supporting parallel algorithms in smaller fault-free cubes. In order to reduce execution slowdown in cube with a given faults, it is essential to identify the maximum healthy sub cubes (maximal incomplete sub cube) in the faulty cube. This paper proposes a new method to identify all the maximal incomplete sub cubes present in a faulty cube taking maximum fault tolerance level i.e. number of faulty nodes is equal to the system dimension. The procedure is a distributed one, as every healthy node next to a failed one performs the same procedure independently and concurrently. Then the reliability expression for the cube is derived. This method is well supported by an efficient algorithm which runs polynomially. The proposed method is found to be simple, general and efficient and thus is applicable to all the cube based topologies**.**

**Index terms****:-**Cube, Maximal Incomplete sub cube, Discarded region, Reliability.

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