Placement delivery arrays for distributed computing (Comp-PDAs) have recently
been proposed as a framework to construct universal computing schemes for
MapReduce-like systems. In this work, we extend this concept to systems with
straggling nodes, i.e., to systems where a subset of the nodes cannot
accomplish the assigned map computations in due time. Unlike most previous
works that focused on computing linear functions, our results are universal and
apply for arbitrary map and reduce functions. Our contributions are as follows.
Firstly, we show how to construct a universal coded computing scheme for
MapReduce-like systems with straggling nodes from any given Comp-PDA. We also
characterize the storage and communication loads of the resulting scheme in
terms of the Comp-PDA parameters. Then, we prove an information-theoretic
converse bound on the storage-communication (SC) tradeoff achieved by universal
computing schemes with straggling nodes. We show that the information-theoretic
bound matches the performance achieved by the coded computing schemes with
straggling nodes corresponding to the Maddah-Ali and Niesen (MAN) PDAs, i.e.,
to the Comp-PDAs describing Maddah-Ali and Niesen's coded caching scheme.
Interestingly, the same Comp-PDAs (the MAN-PDAs) are optimal for any number of
straggling nodes, which implies that the map phase of optimal coded computing
schemes does not need to be adapted to the number of stragglers in the system.
We finally prove that while the points that lie exactly on the fundamental SC
tradeoff cannot be achieved with Comp-PDAs that require smaller number of files
than the MAN-PDAs, this is possible for some of the points that lie close to
the SC tradeoff. For these latter points, the decrease in the requested number
of files can be exponential in the number of nodes of the system.

本文提出了一种基于 Comp-PDAs 框架的通用编码计算方案，用于处理存在滞后节点的 MapReduce 系统，并且证明了该方案可以在任意数量的滞后节点下实现最优性能，同时可以将求解存储和通信负载的问题转化为 Comp-PDAs 参数的表达式。