Cascaded Coded Distributed Computing Schemes Based on Placement Delivery Arrays

Abstract

Li et al. introduced coded distributed computing (CDC) scheme to reduce the communication load in general distributed computing frameworks such as MapReduce. They also proposed cascaded CDC schemes where each output function is computed multiple times, and proved that such schemes achieved the fundamental trade-off between computation load and communication load. However, these schemes require exponentially large numbers of input files and output functions when the number of computing nodes gets large. In this paper, by using the structure of placement delivery arrays (PDAs), we construct several infinite classes of cascaded CDC schemes. We also show that the numbers of output functions in all the new schemes are only a factor of the number of computing nodes, and the number of input files in our new schemes is much smaller than that of input files in CDC schemes derived by Li et al.

Multi-access Coded Caching Scheme with Linear Sub-packetization using PDAs

“…In [13], the authors used placement delivery array (PDA) designs to construct a coded computing scheme and they characterized the storage-computation-communication trade-off, rather than the computation-communication trade-off in [12]. The CDC has been extensively studied in the literature [14]- [24], some of which are based on PDAs [25]- [27]. PDAs are originally introduced in [28] as a solution for coded caching problems, but it is now a widely used design for various problems.…”

Robust incentive mechanisms for efficient and secure coded edge intelligence

“…In addition to the exponential increase in the number of subfiles required, the number of output functions required also increases exponentially as the number of computing nodes in the network increases. There are other methods to reduce the number of subfiles and the number of output functions such as the hypercube computing scheme [76] and the placement delivery array (PDA) [77,78,79]. However, most of the CDC schemes consider non-cascaded systems, i.e., each Reduce function is computed at exactly one computing node [74].…”

“…In [76], a cascaded system is considered but only two values for the number of computing nodes that perform each Reduce function are considered. By applying the concept of PDA to the distributed computation framework, the performance of the proposed computation scheme is evaluated for different number of computing nodes that compute the Reduce functions [77]. Although the implementation of these various methods reduces the number of subfiles generated, it may come at the expense of higher communication load [65], [79].…”

“…Instead of generating infinitely large number of subfiles and distributing them among large number of computing nodes, several studies focus on determining the optimal number of subfiles to avoid the input file from splitting too finely. For example, the resolvable design based schemes [65,74] and PDA approaches [77,78,79] are adopted to split the input files. Hence, it may not be optimal to use all the computing nodes that are connected to the network.…”