无关机器上的分布式负载均衡
Distributed Load Balancing on Unrelated Machines
浏览论文内容
中文总结 AI 辅助
研究分布式CONGEST模型中无关机器的负载均衡问题，提出针对一般作业大小的算法，能在多项对数轮次计算近似分数或整数解，改进了混合装箱 - 覆盖的CONGEST算法，还给出任意混合装箱 - 覆盖线性规划的近似算法。
中文摘要 AI 辅助
我们研究了计算分布式CONGEST模型中著名的负载均衡问题。考虑无关机器设置，每个作业\(j\)为每台机器\(i\)指定一个大小\(s_{ij}\)。目标是找到一个分配\(\varphi: J \to M\)，使最大机器负载最小，机器\(i\)的负载是分配给它的作业的总大小。在CONGEST模型中，目前的最优算法运行在多项对数轮次，并返回Ahmadian、Liu、Peng和Zadimoghaddam（2021）提出的\((1+\varepsilon)\)近似分数解，但该算法及之前的算法仅解决了每个作业在每台机器上大小相同的特殊负载均衡情况。我们的主要贡献是针对一般大小\(s_{ij}\)的算法，该算法能在多项对数轮次中计算出\((1+\varepsilon)\)近似分数解或\((2+\varepsilon)\)近似整数解。由于允许任意边大小后问题结构变化显著，我们的技术与之前分布式负载均衡算法的技术非常不同。我们结果的一个要素是一个具有独立价值的黑箱工具：在CONGEST模型中多项对数轮次内对任意混合装箱 - 覆盖线性规划的\((1+\varepsilon)\)近似算法。这种算法在更强大的并行模型中是已知的，但分布式CONGEST模型中之前的多项对数轮次算法仅解决纯装箱或纯覆盖问题。我们改进了最近用于混合装箱 - 覆盖的\(O(D\,\mathrm{polylog})\)轮CONGEST算法，其中\(D\)是通信图的直径。
英文摘要
We study the well-known load balancing problem in the distributed CONGEST model of computation. We consider the unrelated machines setting, where each job $j$ specifies a size $s_{ij}$ for every machine $i$. We want to find an assignment $φ: J \to M$ minimizing the maximum machine load, where the load of a machine $i$ is the total size of the jobs assigned to it. In the CONGEST model, the state-of-the-art is an algorithm that runs in polylog rounds and returns a $(1+\varepsilon)$-approximate fractional solution from Ahmadian, Liu, Peng, and Zadimoghaddam (2021). However, this algorithm, as well as all previous CONGEST algorithms only solve a special case of load balancing, where each job has the same size on each machine. Our main contribution is an algorithm for general sizes $s_{ij}$. The algorithm computes a $(1+\varepsilon)$-approximate fractional solution or a $(2+\varepsilon)$-approximate integral solution in polylog rounds. The problem structure changes significantly once we allow arbitrary edge-sizes, so our techniques are very different from those used in previous algorithms for distributed load balancing. One ingredient of our result is a black-box tool of independent interest: a $(1+\varepsilon)$-approximation algorithm to arbitrary mixed packing-covering linear programs in the CONGEST model in polylog rounds. such algorithms were known in the more powerful parallel model, but previous polylog-round algorithms in the distributed CONGEST model only solved pure packing or pure covering problems. We improve upon a recent $O(D\,\mathrm{polylog})$-round CONGEST algorithm for mixed packing-covering, where $D$ is the diameter of the communication graph.
