Abstract
Li {\it 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 {\it et al}.
Highlights
W Ith the amount of data being generated increasing rapidly, a computation task could have a huge amount of data to be processed
We focus on cascaded Coded distributed computing (CDC) schemes with smaller numbers of input files and output functions
1) Based on placement delivery array (PDA), which was introduced to construct coded caching schemes in [28], we propose a construction of cascaded CDC schemes
Summary
We give a formulation of our problem. In this system, there are K distributed computing nodes K = {0, 1, . . . , K −1}, N files W = {w0, w1, . . . , wN−1}, where wn ∈ F2D for any n ∈ {0, 1, . . . , N − 1}, and Q output functions Q = {φ0, φ1, . . . , φQ−1}, where φq : FN2D → F2B for any q ∈ {0, 1, . . . , Q − 1}, which maps all the files to FIGURE 1. XK−1 and the IVAs in Ck it computed locally in the map phase, node k could derive × F2lK−1 × F2|CTk| → FN2T where φq ∈ Qk. node k could derive the following IVAs. Schemes and Parameters [16], K, r, s ∈ N+ with 1 ≤ r, s ≤ K [12], K, t ∈ N+ with t ≥ 2 and t|K [30], K, t ∈ N+ with t ≥ 2 and t|K [24], K, t ∈ N+ with t ≥ 2 and t|K. which is enough to compute output value uq = hq We will construct some classes of CDC schemes with smaller numbers of input files and output functions
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