"Short-Dot": Computing Large Linear Transforms Distributedly Using Coded Short Dot Products (1704.05181v1)

Abstract: Faced with saturation of Moore's law and increasing dimension of data, system designers have increasingly resorted to parallel and distributed computing. However, distributed computing is often bottle necked by a small fraction of slow processors called "stragglers" that reduce the speed of computation because the fusion node has to wait for all processors to finish. To combat the effect of stragglers, recent literature introduces redundancy in computations across processors, e.g.,~using repetition-based strategies or erasure codes. The fusion node can exploit this redundancy by completing the computation using outputs from only a subset of the processors, ignoring the stragglers. In this paper, we propose a novel technique -- that we call "Short-Dot" -- to introduce redundant computations in a coding theory inspired fashion, for computing linear transforms of long vectors. Instead of computing long dot products as required in the original linear transform, we construct a larger number of redundant and short dot products that can be computed faster and more efficiently at individual processors. In reference to comparable schemes that introduce redundancy to tackle stragglers, Short-Dot reduces the cost of computation, storage and communication since shorter portions are stored and computed at each processor, and also shorter portions of the input is communicated to each processor. We demonstrate through probabilistic analysis as well as experiments that Short-Dot offers significant speed-up compared to existing techniques. We also derive trade-offs between the length of the dot-products and the resilience to stragglers (number of processors to wait for), for any such strategy and compare it to that achieved by our strategy.

• The paper introduces a novel coded computation method, Short-Dot, that mitigates straggler delays by transforming full dot products into multiple shorter ones.
• It derives key trade-offs between dot product length and straggler resilience, achieving near-optimal performance in distributed computing environments.
• Experimental results, including MNIST digit classification, validate Short-Dot’s efficiency over traditional methods, demonstrating its practical impact in cloud systems.

An Analysis of "Short-Dot": Distributed Computation of Large Linear Transforms

The paper "Short-Dot": Computing Large Linear Transforms Distributedly Using Coded Short Dot Products introduces a novel approach to compute linear transforms in a distributed setting, tackling the prevalent challenge of "stragglers" in large-scale parallel computing systems. The authors propose the Short-Dot method, which, unlike traditional methods, employs a coding-theoretic approach to achieve efficiency in computation, storage, and communication, thereby mitigating the effects of processor delays or failures.

Overview of Challenges

In the current computational landscape, Moore's Law is reaching its limitations, and data dimensions continue to expand, necessitating efficient distributed computing strategies. Conventional methods like Block-Striped Decomposition and the use of Maximum Distance Separable (MDS) codes for computations fail to address the problem of straggler nodes, where the slowest processors can bottleneck the entire system.

Contributions of Short-Dot

Short-Dot addresses these issues by introducing redundancy into the computation process, not by repetition or traditional MDS-based methods, but through a structure that computes numerous short dot products. This method significantly enhances computation speed and reduces stragglers' impact by leveraging the following key innovations:

1. Redundancy through Coded Computation: Instead of distributing the computation of full-length dot products among processors, Short-Dot constructs a larger number of shorter dot products. This reduces the burden on any single processor, allowing computations to proceed effectively even if some processors lag.
2. Trade-off Analysis: The paper derives fundamental limits and trade-offs between the length of dot products and straggler resilience, showing that Short-Dot can approach near-optimal performance in terms of these metrics, especially in large-scale settings.
3. Probabilistic Performance Metrics: Through probabilistic analysis under exponential service-time assumptions, the authors demonstrate that Short-Dot achieves faster computation times compared to uncoded, repetition, and MDS coding strategies. Specifically, Short-Dot outperforms these strategies universally, providing substantial speed-ups as the number of processors increases.
4. Experimental Validation: Experiments conducted on computing clusters reveal that Short-Dot offers significant reductions in computation time for practical tasks, such as classifying handwritten digits in the MNIST database. The empirical results align with theoretical predictions, highlighting Short-Dot's efficiency in mitigating variable straggling effects.

Implications and Future Developments

The implications of Short-Dot are notable in both the theoretical landscape of distributed computing and its practical applications. On the theoretical side, this method refines the understanding of trade-offs between computation redundancy and resilience against delays. Practically, Short-Dot offers a robust approach to handling distributed computation tasks that are susceptible to network latencies and hardware failures—common scenarios in cloud computing and large data centers.

Looking ahead, potential developments could include exploring alternative coding strategies that could further reduce computation times and communication costs. Additionally, investigating the integration of Short-Dot with hardware accelerators, such as GPUs or TPUs, presents a fruitful area for research to push the boundaries of rapid, distributed computation even further.

Short-Dot exemplifies how innovative use of coding theory can transform computational efficiency, and its adoption could become integral in the design of future distributed systems tasked with handling ever-increasing volumes of data.