Algorithm-Based Fault Tolerance for Fail-Stop Failures

• Published in: IEEE transactions on parallel and distributed systems Vol. 19; no. 12; pp. 1628 - 1641
• Main Authors: Zizhong Chen, Dongarra, J.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Checkpointing; Computation; Computational modeling; Computer applications; Failure; Fault tolerance; Fault tolerant systems; Grid computing; Kernel; Lifting equipment; Logging; Mathematical analysis; Mathematical Software; Messages; Multiplication; Parallel algorithms; Redundancy; Reliability and robustness; Studies; Mathematical Software; Parallel algorithms; Reliability and robustness
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/TPDS.2008.58

Fail-stop failures in distributed environments are often tolerated by checkpointing or message logging. In this paper, we show that fail-stop process failures in ScaLAPACK matrix-matrix multiplication kennel can be tolerated without checkpointing or message logging. It has been proved in previous algorithm-based fault tolerance that, for matrix-matrix multiplication, the checksum relationship in the input checksum matrices is preserved at the end of the computation no mater which algorithm is chosen. From this checksum relationship in the final computation results, processor miscalculations can be detected, located, and corrected at the end of the computation. However, whether this checksum relationship can be maintained in the middle of the computation or not remains open. In this paper, we first demonstrate that, for many matrix matrix multiplication algorithms, the checksum relationship in the input checksum matrices is not maintained in the middle of the computation. We then prove that, however, for the outer product version algorithm, the checksum relationship in the input checksum matrices can be maintained in the middle of the computation. Based on this checksum relationship maintained in the middle of the computation, we demonstrate that fail-stop process failures (which are often tolerated by checkpointing or message logging) in ScaLAPACK matrix-matrix multiplication can be tolerated without checkpointing or message logging.