发表机构
Harvard T.H. Chan School of Public Health（哈佛陈曾熙公共卫生学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对网络模块度精确计算这一NP困难问题，提出分支定界算法，通过剪枝部分解保证找到最优聚类，并与暴力法和模拟退火、Louvain方法对比验证了其准确性与效率。
AI 中文摘要
我们考虑网络模块度的计算问题，模块度是衡量网络或图结构的一种常用指标，用于量化网络划分为模块或聚类的程度。网络模块度的计算是一个NP困难问题，因此其精确计算在实践中往往不可行。这导致文献中出现了多种启发式方法。在本工作中，我们借助分支定界算法来精确计算网络模块度。我们的算法保证能找到最大化网络模块度的最优聚类，然而它无需完全探索搜索空间即可实现这一点。这是通过为部分解设定界限，并在可预见部分解不会优于现有解时将其舍弃来实现的。我们评估了所提算法的准确性和运行时间，并将其与暴力求解方法以及两种最先进的基准方法——模拟退火和Louvain方法——进行了比较。
英文摘要
We consider the computation of the network modularity, a common measure of the structure of networks or graphs that quantifies the division of a network into modules or clusters. The computation of the network modularity is an NP-hard problem, thus making its exact computation often infeasible in practice. This has resulted in the development of several heuristics in the literature. In this work, we consider the exact computation of the network modularity with the help of a branch-and-bound algorithm. Our algorithm is guaranteed to find the optimal clustering that maximizes the network modularity, however it achieves this without a full exploration of the search space. This is accomplished by bounding partial solutions and discarding them if it can be foreseen that a partial solution will not yield an improvement over an existing solution. We assess our algorithm with respect to accuracy and runtime and compare it to a brute-force approach as well as two state-of-the-art benchmarks, simulated annealing and the Louvain method.
