Maximizing (k,L)-Core With Edge Augmentation in Multilayer Graphs

• Published in: IEEE transactions on computational social systems Vol. 11; no. 3; pp. 3931 - 3943
• Main Authors: Chang, Chih-Chieh, Lu, Chia-Hsun, Teng, Shun-Jen, Chang, Ming-Yi, Ho, Ya-Chi, Shen, Chih-Ya
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.06.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> (k; Algorithms; Graph augmentation; Graph theory; Graphs; Image edge detection; L)</tex-math> </inline-formula>-core; multilayer graphs; Multilayers; Nonhomogeneous media; Optimization; Performance evaluation; Polynomials; Search problems; Size measurement; Social networking (online); Space exploration
• ISSN: 2329-924X; 2373-7476
• DOI: 10.1109/TCSS.2023.3332091

While most previous work pays attention on extracting dense subgraphs, such as <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-cores, we argue that augmenting the graph to maximize the size of dense subgraphs is also very important and finds many applications. Therefore, in this article, we study the dense subgraph augmentation problem in multilayer graphs. Specifically, we propose the notion of <inline-formula><tex-math notation="LaTeX">(k,L)</tex-math></inline-formula>-core to model the dense subgraphs in multilayer graphs and propose a new research problem, budgeted maximal <inline-formula><tex-math notation="LaTeX">(k,L)</tex-math></inline-formula>-core augmentation (BMA) problem, which adds at most <inline-formula><tex-math notation="LaTeX">b</tex-math></inline-formula> edges in the multilayer graphs to maximize the size of <inline-formula><tex-math notation="LaTeX">(k,L)</tex-math></inline-formula>-core. We prove the NP-hardness of the general BMA problem when <inline-formula><tex-math notation="LaTeX">k\geq 2</tex-math></inline-formula> and devise a polynomial-time algorithm to find the optimal solution for a special case of BMA, i.e., <inline-formula><tex-math notation="LaTeX">(2,1)</tex-math></inline-formula>-BMA. We then devise an effective algorithm, named search for optimum and reorder adaptively (SORA), with various performance-improving strategies to tackle the general BMA problem. We evaluate the performance of the proposed approaches on multiple large-scale datasets and compare them with the state-of-the-art baselines. Experimental results indicate that our proposed approaches significantly outperform the baselines in terms of solution quality and efficiency.