Order Optimal Cascaded Coded Distributed Computing with Low Complexity and Improved Flexibility

Coded distributed computing (CDC), introduced by Li et al., effectively reduces communication load in MapReduce systems. In cascaded CDC with $K$ nodes, $N$ input files, and $Q$ output functions, each input file is mapped by $r \geq 1$ nodes, and each output function is computed by $s>1$ nodes, enabling coding for multicast opportunities. However, existing CDC schemes often require splitting data into exponentially many files or functions as $K$ grows, increasing complexity and degrading performance. This paper addresses the case of $K / s \in \mathbb{N}$, proposing a low-complexity CDC scheme through carefully designing the strategies of data placement and output function assignment. The proposed scheme offers key advantages: $\mathbf{1}$) multicast gains of $(r+s-1)(1-1 / s)$ and approximately $r+s-1$ for large $s$, with better communication load than the well-known Li et al.'s scheme; 2) reduce input and output file requirements; and 3) binary field $\mathbb{F}_{2}$ operations implement in a one-shot manner, enabling immediate decoding. We also derive a new information-theoretic bound under the proposed strategies, showing that the communication load is order-optimal within a factor of 2 and approximately optimal when $K$ is sufficiently large for a given $r$.