基于迭代重着色的分布式图着色
On Distributed Graph Coloring with Iterative Recoloring
摘要：
在许多并行应用程序中，确定可以同时执行的操作集是一个重要的问题。通过将操作及其交互建模为图，可以通过解决图着色问题来识别独立操作。许多有效的顺序算法是已知的这个NP完全问题，但它们通常是不适合的操作和它们的相互作用时，分布在大型并行计算机的内存中。在现有的分布式内存图着色算法的基础上，本文研究了两种兼容的技术，用于快速和可扩展的分布式内存图着色。首先，我们介绍了一种改进的分布式后处理操作，所谓的优化，这大大提高了颜色的数量。我们提出了一种新颖而有效的通信方案，使其能够优雅地扩展。重新着色必须使用图形的现有着色作为种子。我们的第二个贡献是引入一个随机的初始着色的颜色选择策略，快速产生解决方案的质量适中。我们广泛评估我们的新技术对现有分布式算法的影响，并显示时间质量的权衡。我们表明，结合初始随机着色与多个并行迭代产生更好的质量解决方案，在大规模的较小的运行时间。
英文摘要：
Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent operations by solving a graph coloring problem. Many efficient sequential algorithms are known for this NP-Complete problem, but they are typically unsuitable when the operations and their interactions are distributed in the memory of large parallel computers. On top of an existing distributed-memory graph coloring algorithm, we investigate two compatible techniques in this paper for fast and scalable distributed-memory graph coloring. First, we introduce an improvement for the distributed post-processing operation, called recoloring, which drastically improves the number of colors. We propose a novel and efficient communication scheme for recoloring which enables it to scale gracefully. Recoloring must be seeded with an existing coloring of the graph. Our second contribution is to introduce a randomized color selection strategy for initial coloring which quickly produces solutions of modest quality. We extensively evaluate the impact of our new techniques on existing distributed algorithms and show the time-quality tradeoffs. We show that combining an initial randomized coloring with multiple recoloring iterations yields better quality solutions with the smaller runtime at large scale.
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