Algorithm-based recovery for iterative methods without checkpointing

In today's high performance computing practice, fail-stop failures are often tolerated by checkpointing. While checkpointing is a very general technique and can often be applied to a wide range of applications, it often introduces a considerable overhead especially when computations reach petascale and beyond. In this paper, we show that, for many iterative methods, if the parallel data partitioning scheme satisfies certain conditions, the iterative methods themselves will maintain enough inherent redundant information for the accurate recovery of the lost data without checkpointing. We analyze the block row data partitioning scheme for sparse matrices and derive a sufficient condition for recovering the critical data without checkpointing. When this sufficient condition is satisfied, neither checkpoint nor roll-back is necessary for the recovery. Furthermore, the fault tolerance overhead (time) is zero if no actual failures occur during a program execution. Overhead is introduced only when an actual failure occurs. Experimental results demonstrate that, when it works, the proposed scheme introduces much less overhead than checkpointing on the current world's eighth-fastest supercomputer Kraken.