Graph edit distance (GED) is an important metric for measuring the distance or similarity between two graphs. It is defined as the minimum number of edit operations required to transform one graph into another. Computing the exact GED between two graphs is an NP-hard problem. With the success of deep learning across various application domains, graph neural networks have also been recently utilized to predict the GED between graphs. However, the existing studies on learning-based methods have two significant limitations. (1)~The development of deep learning models for GED prediction has been explored in various research fields (e.g., databases, machine learning, information retrieval, and computer vision), yet cross-field evaluations have been quite limited. (2)~More importantly, all these advancements have been evaluated against a simple combinatorial heuristic baseline, with their models shown to outperform it. In this paper, we aim to bridge this knowledge gap. We first conduct a holistic review of the existing learning-based methods, categorizing them into non-interpretable and interpretable GED prediction approaches, while highlighting their overarching design principles and relationships among these models. Secondly, we present a simple yet effective combinatorial heuristic algorithm App-BMao for GED estimation, adapted from an existing exact GED computation algorithm. App-BMao provides interpretable GED estimation with controlled time and space complexity. Extensive empirical evaluations on three widely used datasets show that the new heuristic algorithm App-BMao outperforms all existing learning-based approaches for both interpretable and non-interpretable GED prediction.

The k -plex model is a relaxation of the clique model by allowing every vertex to miss up to k neighbors. Designing exact and efficient algorithms for computing a maximum k -plex in a graph has been receiving increasing interest recently. However, the existing algorithms are still inefficient due to having major limitations. We in this paper design a new algorithm kPlexS for the maximum k -plex problem, with three novel contributions. Firstly, we propose a new framework for computing maximum k -plex over large sparse graphs, by iteratively extracting small dense subgraphs from it and then solving each of the extracted dense subgraphs by a branch-and-bound search. Secondly, we propose an efficient reduction algorithm CTCP to reduce the input graph size by exhaustively conducting vertex reduction and edge reduction. CTCP computes a smaller reduced graph and also has a lower time complexity than the existing techniques. Moreover, we iteratively invoke CTCP to reduce the input graph once a vertex has been processed and removed from it. Thirdly, we develop a branch-and-bound algorithm BBMatrix specifically targeting the dense subgraphs that are extracted from the input graph. BBMatrix represents its input graph by an adjacency matrix, and utilizes both first-order (i.e., individual vertices) and second-order information (i.e., pairs of vertices) for reduction and upper bounding. In addition, incremental techniques are proposed to efficiently apply the reduction and upper bounding during the recursion. Extensive empirical studies on large real graphs demonstrate that our algorithm kPlexS outperforms the state-of-the-art algorithms BnB, Maplex, and KpLeX.