图算法的爱因斯坦求和启用设计空间：广度优先搜索案例研究
The Einsum-Enabled Design Space for Graph Algorithms: A BFS Case Study
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中文总结 AI 辅助
该研究提出基于EDGE的方法推理图算法实现，以BFS为案例，探索多种优化选择变体，既能表示已有算法技术，还发现新变体，在中到高归一化度方差图上性能比基线提升1.2至1.7倍。
中文摘要 AI 辅助
我们提出一种有原则的方法来推理各种图算法实现。利用扩展的通用爱因斯坦求和表示法（EDGE），它能让我们沿代数操作、映射、格式和低级实现这四个轴分解复杂度。以广度优先搜索（BFS）为例进行案例研究，应用该方法探索了基于GPU实现的26类优化选择中的90多种变体。除了表明我们的方法足以表示如BFS拉取变体等先前发现的算法技术外，还发现了新变体，对于具有中到高归一化度方差的图，其几何平均性能比最佳Gunrock基线变体提升了1.2倍至1.7倍。
英文摘要
We propose a principled approach to reasoning about various graph algorithm implementations. We leverage the extended general Einsum notation (EDGE) which allows us to factor complexity along four axes: algebraic manipulation, mapping, format, and low-level implementations. Using breadth-first search (BFS) as a driving example and case study, we apply our methodology to explore over 90 variations across 26 categories of optimization choices for our GPU-based implementations. In addition to showing that our approach is general enough to represent previously discovered algorithmic techniques such as the pull variant of BFS, we discover novel variants that lead to geomean performance benefits ranging from 1.2x to 1.7x over the best Gunrock baseline variation for graphs with mid- to high- normalized degree variance.
