Sliding Substitution of Failed Nodes

This paper considers the questions of how spare nodes should be allocated, how to substitute them for faulty nodes, and how much the communication performance is affected by such a substitution. The third question stems from the modification of the rank mapping by node substitutions, which can incur additional message collisions. In a stencil computation, rank mapping is done in a straightforward way on a Cartesian network without incurring any message collisions. However, once a substitution has occurred, the node- rank mapping may be destroyed. Therefore, these questions must be answered in a way that minimizes the degradation of communication performance. In this paper, several spare-node allocation and nodesubstitution methods will be proposed, analyzed, and compared in terms of communication performance following the substitution. It will be shown that when a failure occurs, the peer-to-peer (P2P) communication performance on the K computer can be slowed by a factor of three and collective performance can be cut in half. On BG/Q, P2P performance can be slowed by a factor of five and collective performance can be slowed by a factor of ten. However, those numbers can be reduced by using an appropriate substitution method.