Self- Discovery on heirarchical three dimensional focus.

The advances in technology have made it possible to build massively parallel supercomputers connected using interconnection networks.

IBM's Blue-Gene/L (BG/L) machine with $2^{16}$ processors operating at 180 TFLOPS is a good example. BG/L is planned to have a three dimensional torus topology. The process of discovering size of a machine, assigning consistent, and unique spatial coordinates to the processors for identification, is called {\it self-discovery}. An automated, and distributed fault-tolerant algorithm to achieve self-discovery is very important for operation of such a system. For scalability and modularity, the system is built hierarchically using smaller cubes. Hierarchically carrying out self-discovery in this system poses a unique problem: the orientations of two adjacent toruses may not match, resulting in {\it disorientation}.

In this paper, we present an autonomic distributed algorithm that hierarchically achieves self-discovery on a BG/L machine of previously unknown size, unknown extent along its dimensions, node failures, and link failures. It assigns consistent, and unique $(x,y,z)$ coordinate to every node which is functioning. We analyze the probability of failure of our algorithm in the presence of faults.