Order Optimal Task Allocation in Distributed Computing via Interweaved Cliques
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914491831156736 |
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| author | Maheri, Javad Namboodiri, K. K. Krishnan Elia, Petros |
| author_facet | Maheri, Javad Namboodiri, K. K. Krishnan Elia, Petros |
| contents | We consider a distributed computing system in which a master node coordinates $N$ workers to evaluate a function over $n$ input files, where this function accepts general decomposition. In particular, we focus on the general case where the requested function admits a $d$-uniform decomposition, meaning that it can be decomposed into a set of subfunctions that each depends on a unique $d$-tuple of the $n$ files. Our objective is to design file and task allocations that minimize the worst-case communication from the master to any worker and the worst-case computational load across workers. We first show that the optimal file and task allocation with minimum communication and computation costs admits a natural characterization within combinatorial design theory: it corresponds to a Steiner system $S(t, k, v)$ with $t=d$, $v=n$, and $k \approx \frac{n}{N^{1/d}}$. However, Steiner systems are known to exist only for very restricted parameter regimes. To overcome this limitation, we propose the information-theoretic-inspired \emph{Interweaved Clique (IC) design}, a universal and deterministic allocation framework that relaxes the strict structure of Steiner systems by allowing slight variations in worker file loads. Although slightly suboptimal, the IC design achieves a communication cost within a constant factor $4e$ from our converse, while also maintaining an order-optimal computation cost, thus allowing this work to derive the fundamental scaling laws of this general distributed computing problem for a large range of parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18232 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Order Optimal Task Allocation in Distributed Computing via Interweaved Cliques Maheri, Javad Namboodiri, K. K. Krishnan Elia, Petros Information Theory We consider a distributed computing system in which a master node coordinates $N$ workers to evaluate a function over $n$ input files, where this function accepts general decomposition. In particular, we focus on the general case where the requested function admits a $d$-uniform decomposition, meaning that it can be decomposed into a set of subfunctions that each depends on a unique $d$-tuple of the $n$ files. Our objective is to design file and task allocations that minimize the worst-case communication from the master to any worker and the worst-case computational load across workers. We first show that the optimal file and task allocation with minimum communication and computation costs admits a natural characterization within combinatorial design theory: it corresponds to a Steiner system $S(t, k, v)$ with $t=d$, $v=n$, and $k \approx \frac{n}{N^{1/d}}$. However, Steiner systems are known to exist only for very restricted parameter regimes. To overcome this limitation, we propose the information-theoretic-inspired \emph{Interweaved Clique (IC) design}, a universal and deterministic allocation framework that relaxes the strict structure of Steiner systems by allowing slight variations in worker file loads. Although slightly suboptimal, the IC design achieves a communication cost within a constant factor $4e$ from our converse, while also maintaining an order-optimal computation cost, thus allowing this work to derive the fundamental scaling laws of this general distributed computing problem for a large range of parameters. |
| title | Order Optimal Task Allocation in Distributed Computing via Interweaved Cliques |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.18232 |