This document proposes a new approach called numerical packing to mitigate core failures in integer sum-of-product computations on cloud computing systems. Numerical packing produces redundant results within the numerical representation of outputs, differing from existing checksum approaches that require separate checksum results. This new approach imposes a 37.5% reduction in maximum output bitwidth compared to 32-bit integer representations, while enabling mitigation of up to one quadcore failure with comparable processing throughput to conventional failure-intolerant routines and superior throughput to checksum-based approaches. When used in an image retrieval framework on AWS spot instances, the proposed approach leads to 16-23% cost reduction against checksum methods and over 70% reduction versus failure-intolerant processing on higher-

1. Core Failure Mitigation in Integer Sum-of-Product Computations on Cloud
Computing Systems
Abstract:
The decreasing mean-time-to-failure estimates in cloud computing systems
indicate that multimedia applications running on such environments should be
able to mitigate an increasing number of core failures at runtime. We propose a
new roll-forward failure-mitigation approach for integer sum-of-product
computations, with emphasis on generic matrix multiplication (GEMM) and
convolution/crosscorrelation (CONV) routines. Our approach is based on the
production of redundant results within the numerical representation of the
outputs via the use of numerical packing. This differs from all existing roll-forward
solutions that require a separate set of checksum (or duplicate) results. Our
proposal imposes 37.5% reduction in the maximum output bitwidth supported in
comparison to integer sum-of-product realizations performed on 32-bit integer
representations which is comparable to the bitwidth requirement of checksum-
methods for multiple core failure mitigation. Experiments with state-of-the-art
GEMM and CONV routines running on a c4.8xlarge compute-optimized instance
of amazon web services elasticcompute cloud (AWS EC2) demonstrate that the
proposed approach is able to mitigate up to one quadcore failure while achieving
processing throughput that is: 1) comparable to that of the conventional, failure-
intolerant, integer GEMM and CONV routines, 2) substantially superior to that of
the equivalent roll-forward failure-mitigation method based on checksum
streams. Furthermore, when used within an image retrieval framework deployed

2. over a cluster of AWS EC2 spot (i.e., low-cost albeit terminatable) instances, our
proposal leads to: 1) 16%-23% cost reduction against the equivalent checksum-
based method and 2) more than 70% cost reduction against conventional failure-
intolerant processing on AWS EC2 on-demand (i.e., higher-cost albeit guaranteed)
instances.