In the digital era, users typically interact with diverse items across multiple domains (e.g., e-commerce, streaming platforms, and social networks), generating intricate heterogeneous interaction graphs. Leveraging multi-domain data can improve recommendation systems by enriching user insights and mitigating data sparsity in individual domains. However, integrating such multi-domain knowledge for cross-domain recommendation remains challenging due to inherent disparities in user behavior and item characteristics and the risk of negative transfer, where irrelevant or conflicting information from the source domains adversely impacts the target domain's performance. To tackle these challenges, we propose HAGO, a novel framework with Heterogeneous Adaptive Graph coOrdinators, which dynamically integrates multi-domain graphs into a cohesive structure. HAGO adaptively adjusts the connections between coordinators and multi-domain graph nodes to enhance beneficial inter-domain interactions while alleviating negative transfer. Furthermore, we introduce a universal multi-domain graph pre-training strategy alongside HAGO to collaboratively learn high-quality node representations across domains. Being compatible with various graph-based models and pre-training techniques, HAGO demonstrates broad applicability and effectiveness. Extensive experiments show that our framework outperforms state-of-the-art methods in cross-domain recommendation scenarios, underscoring its potential for real-world applications. The source code is available at https://github.com/zhy99426/HAGO.

Attributed Hypergraph Clustering (AHC) aims at partitioning a hypergraph into clusters such that nodes in the same cluster are close to each other with both high connectedness and homogeneous attributes. Existing AHC methods are all based on matrix factorization which may incur a substantial computation cost; more importantly, they inherently require a prior knowledge of the number of clusters as an input which, if inaccurately estimated, shall lead to a significant deterioration in the clustering quality. In this paper, we propose Attributed Hypergraph Representation for Clustering (AHRC), a cluster-number-free hypergraph clustering consisting of an effective integration of the hypergraph topology and node attributes for hypergraph representation, a multi-hop modularity function for optimization, and a hypergraph sparsification for scalable computation. AHRC achieves cutting-edge clustering quality and efficiency: compared to the state-of-the-art (SOTA) AHC method on 10 real hypergraphs, AHRC obtains an average of 20% higher F-measure, 24% higher ARI, 26% higher Jaccard Similarity, 10% higher Purity, and runs 5.5× faster. As a byproduct, the intermediate result of graph representation dramatically boosts the clustering quality of SOTA contrastive-learning-based hypergraph clustering methods, showing the generality of our graph representation.

Query optimization is a complex planning and decision-making problem within the exponentially growing plan space in database management systems (DBMS). Traditional optimization techniques have been extensively studied over decades, leaving limited room for further improvement along this track. Recent developments of Large Language Models (LLMs) have demonstrated their potential in solving complex planning and decision-making problems, such as arithmetic and programmatic tasks. In this paper, we try to explore the potential of LLMs in handling query optimization and propose a tentative LLM-based query optimizer dubbed LLM-QO, established on PostgreSQL's execution engine. In LLM-QO, we formulate query optimization in an autoregressive fashion which directly generates the execution plan without explicit plan enumeration. To investigate the essential input of LLM-QO, we design a customized data recipe named QInstruct to collect the training data from various optimizers and serialize the database's meta data, queries and corresponding plans into a textual format. Based on QInstruct, we implement a two-stage fine-tuning pipeline, Query Instruction Tuning (QIT) and Query Direct Preference Optimization (QDPO), to empower the capability of general-purpose LLMs in handling query optimization. In our experiments, LLM-QO can generate valid and high-quality plans and consistently outperforms both traditional and learned optimizers on three query workloads. Our findings verify that LLMs can be derived as query optimizers where generalization, efficiency and adaptivity deserve further research efforts.

A cohesive subgraph of k-truss requires that each edge has at least$(k-2)$triangles, which has wide applications of modeling social communities and complex network visualization. Recently, the study of truss maximization has gained attention, which aims to enlarge$k$-truss most by inserting$b$new edges into a graph$G$. However, existing maximization methods suffer from a stiff strategy of complete truss conversion, that is either converting the whole$(k-1)$-truss component to k-truss or converting no edge to k-truss without using any budget. To tackle this bottleneck, we develop a novel partial conversion strategy to explore more insertion plans. Based on partial conversion strategy, we revisit the problem of truss maximization in this paper and propose adaptive solutions by achieving more new k-truss edges. Specifically, we first decompose all$(k-1)$-truss into a series of disjoint components via the triangle connectivity, where each component's conversion is independent to each other. Then, for each$(k-1)$-truss component, we explore possible insertion plans of partial conversions. An intuitive method is to randomly insert a budget no more than$b$new edges and check the expected profit of new$k$-truss edges. Obviously, this method is inefficient due to a large search space of edge insertions and many times of expensive$k$-truss verification. To improve it, we propose a new minimum-cut based approach, which converts a subgraph of$(k-1)$-truss component into a flow graph with weighted edges and finds a key of maximum-flow answer corresponding to a k-truss conversion plan with the minimum budget consumption. Next, we develop a new dynamic programming framework to find the best way to allocate the budget$b$to all components. We design two fast dynamic programming algorithms and analyze the complexities theoretically. In addition, we explore the case of a large given budget$b$and extend our techniques to handle the conversion of$(k-h)$-truss into$k$-truss for$2\leq h\leq k-2$. Extensive experiment results demonstrate the superiority of our algorithms against the state-of-the-art methods.

Graph edit distance (GED) computation is a fundamental NP-hard problem in graph theory. Given a graph pair ( G 1 , G 2 ), GED is defined as the minimum number of primitive operations converting G 1 to G 2 . Early studies focus on search-based inexact algorithms such as A*-beam search, and greedy algorithms using bipartite matching due to its NP-hardness. They can obtain a sub-optimal solution by constructing an edit path (the sequence of operations that converts G 1 to G 2 ). Recent studies convert the GED between a given graph pair ( G 1 , G 2 ) into a similarity score in the range (0, 1) by a well designed function. Then machine learning models (mostly based on graph neural networks) are applied to predict the similarity score. They achieve a much higher numerical precision than the sub-optimal solutions found by classical algorithms. However, a major limitation is that these machine learning models cannot generate an edit path. They treat the GED computation as a pure regression task to bypass its intrinsic complexity, but ignore the essential task of converting G 1 to G 2 . This severely limits the interpretability and usability of the solution. In this paper, we propose a novel deep learning framework that solves the GED problem in a two-step manner: 1) The proposed graph neural network GEDGNN is in charge of predicting the GED value and a matching matrix; and 2) A post-processing algorithm based on k -best matching is used to derive k possible node matchings from the matching matrix generated by GEDGNN. The best matching will finally lead to a high-quality edit path. Extensive experiments are conducted on three real graph data sets and synthetic power-law graphs to demonstrate the effectiveness of our framework. Compared to the best result of existing GNN-based models, the mean absolute error (MAE) on GED value prediction decreases by 4.9% ~ 74.3%. Compared to the state-of-the-art searching algorithm Noah, the MAE on GED value based on edit path reduces by 53.6% ~ 88.1%.

Given two sets of vertices Sa and Sb of a graph, computing their common vertices, namely set intersection, is one primitive operation in many graph algorithms such as triangle counting, maximal clique enumeration, and subgraph matching. Thus, accelerating set intersections is beneficial to these algorithms. In the paper, we propose a novel reducing-merging framework for set intersections over graphs rather than intersecting the two sets directly. In the reducing phase, the vertices that cannot fall into the intersection are screened out by applying the range reduction. Based on the truncated subsets, the intersection can be easily obtained using the classic merging algorithm. To optimize the range codes that sketch the vertices, we formulate the problem of range code optimization and prove its NP-hardness. We develop efficient yet effective algorithms for two typical scenarios global intersection and local intersection. Moreover, we present a novel two-level merging algorithm to enhance the performance. The results of extensive experiments over real graphs show that our approach can achieve significant speedups compared to the merge-based algorithm.

As a fundamental NP-hard problem in graph theory, the maximum independent set (MIS) has attracted a lot of efforts to improve the time efficiency. However, most graphs in real scenarios are usually changing over time. But the previous studies take the stationary graphs as input, the computation of MIS in dynamic graphs receives little attention. Since computing the exact MIS is intractable, we compute the high-quality (large-size) independent set for dynamic graphs in this paper, where 4 graph updating operations are allowed: adding or deleting a vertex or an edge. Based on two state-of-the-art reduction rules that are designed for static graphs, we propose a novel scheme, i.e., dependency graph based independent set computation, which can support computing the high-quality independent set on the basis of the previous result rather than calculating from scratch. Moreover, a dynamic searching strategy is devised to improve time efficiency. In order to make it more useful in practical applications, we devise an effective yet efficient method to deal with the batch update. To confirm the effectiveness and efficiency of the proposed methods, we conduct extensive experiments over both real and synthetic datasets.