Maximum vertex weight clique problem (MVWCP) and maximum edge weight clique problem (MEWCP) are two significant generalizations of maximum clique problem (MCP), and can be widely used in many real-world applications including molecular biology, broadband network design and pattern recognition. Recently, breakthroughs have been made for solving MVWCP in large graphs, resulting in several state-of-the-art algorithms, such as WLMC, FastWClq and LSCC + BMS. However, less attention has been paid to solving MEWCP in large graphs. In this paper, we present an efficient Stochastic Local Search (SLS) algorithm for MEWCP by combining clique construction, local search and graph reduction, resulting in a new algorithm named ReConSLS. We also propose a new upper bound function for edge weighted graphs which is essential for graph reduction. Extensive experiments on a wide range of large graphs demonstrate that ReConSLS surpasses state-of-the-art SLS competitors on the majority of testing graphs.

中文翻译：

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解决大图中最大边缘权集团问题的有效局部搜索算法

最大顶点权重集团问题（MVWCP）和最大边缘权重集团问题（MEWCP）是最大集团问题（MCP）的两个重要概括，可以广泛用于许多实际应用中，包括分子生物学，宽带网络设计和模式识别。最近，在解决大型图中的MVWCP方面取得了突破，从而产生了几种最新算法，例如WLMC，FastWClq和LSCC + BMS。但是，在大型图中求解MEWCP的关注较少。在本文中，我们通过结合集团构造，局部搜索和图约简，提出了一种有效的MEWCP随机局部搜索（SLS）算法，从而产生了一种名为ReConSLS的新算法。我们还为边缘加权图提出了一个新的上界函数，这对于图归约至关重要。