基于双连通分量覆盖图的稀疏大图最大流并行加速方法

Engineering Bi-Connected Component Overlay for Maximum-Flow Parallel Acceleration in Large Sparse Graph

最大流问题是图论中重要的基础性问题,大规模网络中的最大流加速已成为重要研究方向,已有工作包括并行计算加速和图缩减加速2种思路,但仍有较大改进空间:(1)图缩减和并行计算2种加速思路并未充分融合,导致各自加速效果受限;(2)已有加速算法对常见的多次最大流求解支持不足,导致多次计算间存在大量冗余工作;(3)已有加速算法往往需涉及出入度和边容量等多个条件,计算复杂度偏高。针对上述问题,提出了一种基于优化子图的最大流并行加速方法,通过识别原始大图的双连通分量并建立覆盖图,可将任意最大流问题分解为独立的子问题,并行求解快速获取最大流精确解;覆盖图的构建仅涉及节点之间连接关系,具较低的时间复杂度。在基准图上的测试结果表明,算法可显著缩短稀疏大图中最大流计算时间。

Network maximum flow problem is important and basic in graph theory,and one of its research directions is maximum-flow acceleration in large-scale graph.Existing acceleration strategy includes graph contraction and parallel computation,where there is still room for improvement:(1)The existing two acceleration strategies are not fully integrated,leading to their limited acceleration effect;(2)There is no sufficient support for computing multiple maximum-flow in one graph,leading to a lot of redundant computation.(3)The existing preprocessing methods need to consider node degrees and capacity constraints,resulting in high computational complexity.To address above problems,we identify the bi-connected components in a given graph and build an overlay,which can help split the maximum-flow problem into several subproblems and then solve them in parallel.The algorithm only uses the connectivity in the graph and has low complexity.The analyses and experiments on benchmark graphs indicate that the method can significantly shorten the calculation time in large sparse graphs.