# Single-Forking of Coded Subtasks for Straggler Mitigation

### Ajay Kumar Badita

**SUMMARY OF RESEARCH**

I. MOTIVATION

Motivated by scalability, availability, and reliability, there has been a paradigm shift from centralized computation at a large supercomputer to distributed computing on a large cluster of regular compute servers to perform complex tasks. In distributed compute setting, a single task is fragmented into a smaller number of subtasks, and processed by the compute cluster. Task completion time is limited by the slowest execution time of the parallel subtasks. The lagging subtasks are referred to as stragglers, and they delay the entire task execution. Straggling servers is one of the challenges in distributed computing. Redundancy has emerged as a popular technique to mitigate the impact of stragglers. Redundant compute subtasks can be sent to a larger set of compute nodes, such that a smaller subset suffices for the task completion. This approach can be used for straggler mitigation in the face of uncertainty in task execution times at the compute nodes. Coding theoretic techniques can be employed to systematically control the redundancy in storage and compute systems.

II. RELEVANT WORK AND RESEARCH GAP A popular redundancy technique to mitigate stragglers in distributed computing system is replication, where each of the finite k subtasks of a task can be replicated to n k servers each [1]. However, the task will only be done if one sever from each of the n k partitions finish processing their corresponding replicated subtasks. Contrastingly, we have an efficient redundancy technique called maximum distance separable (MDS) coding [2], in which a task is fragmented into k subtasks and encoded into n coded subtasks, where completion of any k coded subtasks finishes the original task. MDS coding is a more general form of redundancy than simple replication. It has been shown that this more flexible redundancy scheme can be employed for certain computing tasks in distributed compute systems [2]–[5]. For a single task system, it was shown in [6] that MDS codes are the latency-minimizing code among a class of symmetric codes. Straggler mitigation using coding theoretic techniques for matrix multiplication has been achieved in [2]–[4]. We observe that redundancy can mitigate the impact of stragglers, however it comes at the cost of additional compute nodes working on redundant coded subtasks. This cost can be measured by the amount of work done by all compute nodes, called aggregate server utilization. This cost has not been taken into account by the previous works in the literature. In a proactive mitigation approach, we attempt to show that server utilization can be reduced by dynamic coded redundancy, where the number of redundant servers available to a task changes with time.

III. PROBLEM DESCRIPTION AND RESULTS We are interested in dynamic coded redundancy for a single compute task with coded subtasks. In dynamic coded redundancy, additional redundant coded subtasks are spawned on individual compute nodes, adaptively over time. The instants at which coded subtasks are spawned are referred to as forking points. We are interested in optimal adaptive strategy such that a linear combination of the mean task completion time and the mean server utilization is minimized. Specifically, we address following two interdependent questions: 1) How should we select the forking points? 2) How many coded subtasks should be initiated at each forking point? Consider a single task divided into k subtasks and coded into n coded subtasks using a fixed (n, k) MDS block code, where each subtask is sent to a unique compute server. One option is to start all n coded subtasks at time 0, corresponding to the task request time. This leads to using all n servers until the first k of them have finished, resulting in low task completion time at the cost of a high server utilization. Another option is to use only k servers and start with all of them at time 0. This would help avoid the excess server utilization for the remaining n − k servers, resulting in low server utilization cost and larger task completion time. To be specific, in single-forking, a flexible approach is to start with n0 < n coded subtasks at time 0. When `0 < k of them are finished, we launch the remaining n1 = n − n0 servers at the single forking point. We propose a dynamic strategy, where coded subtasks of an unfinished task are sequentially initiated at forking points. In this case, there exists an optimal number of initial servers from which the file should be downloaded. Our analytical study was for lightly-tailed shifted exponential download times. However, we empirically verified that the insights from our theoretical study continue to hold true for heavy-tailed distributions for download times. In addition, we performed experiments on a real compute cluster, and verified that the theoretical insights continue to hold true.

**REFERENCES**

[1] D. Wang, G. Joshi, and G. W. Wornell, “Efficient straggler replication in large-scale parallel computing,” ACM Trans. Model. Perform. Eval. Comput. Syst. (TOMPECS), vol. 4, no. 2, Apr. 2019. [2] K. Lee, M. Lam, R. Pedarsani, D. Papailiopoulos, and K. Ramchandran, “Speeding up distributed machine learning using codes,” IEEE Trans. Inf. Theory, vol. 64, no. 3, pp. 1514–1529, March 2018. [3] S. Dutta, V. Cadambe, and P. Grover, “Short-dot: Computing large linear transforms distributedly using coded short dot products,” IEEE Trans. Inf. Theory, vol. 65, no. 10, pp. 6171–6193, 2019. [4] Q. Yu, M. A. Maddah-Ali, and A. S. Avestimehr, “Straggler mitigation in distributed matrix multiplication: Fundamental limits and optimal coding,” IEEE Trans. Inf. Theory, vol. 66, no. 3, pp. 1920–1933, 2020. [5] K. Lee, R. Pedarsani, D. Papailiopoulos, and K. Ramchandran, “Coded computation for multicore setups,” in IEEE Inter. Symp. Inf. Theory (ISIT), 2017, pp. 2413–2417. [6] A. G. Dimakis, P. B. Godfrey, Y. Wu, M. J. Wainwright, and K. Ramchandran, “Network coding for distributed storage systems,” IEEE Trans. Inf. Theory, vol. 56, no. 9, pp. 4539–4551, 2010.

LIST OF ALL PUBLICATIONS DURING THE FELLOWSHIP YEAR

**Journal article**

• Ajay Badita, Parimal Parag, and Vaneet Aggarwal. Single-forking of coded subtasks for straggler mitigation, IEEE/ACM Transactions on Networking, July 2021.

**BibTex format** Attached in the zip file.

**Online link to the paper** https://ieeexplore.ieee.org/document/9472871

**pdf copy of the paper** Attached in the zip file