团划分问题的紧上界子网络约束及精确解

Pub Date : 2023-09-09 DOI:10.1007/s00186-023-00835-y
Alexander Belyi, Stanislav Sobolevsky, Alexander Kurbatski, Carlo Ratti
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引用次数: 1

摘要

摘要考虑了完全加权图聚类问题的一个变体。其目的是将节点划分为集群,最大化集群内边缘权重的总和。这个问题被称为团划分问题,在具有不同符号的边权的一般情况下是np困难的。我们提出了一种新的估计目标函数上界的方法,并结合经典的分支定界方法来求精确解。我们在广泛的随机图和现实世界的网络上评估了我们的方法。与已知的替代方法相比,该方法提供了更严格的上界,并取得了显着的收敛速度提高。
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Subnetwork constraints for tighter upper bounds and exact solution of the clique partitioning problem
Abstract We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.
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