Graph Matching Research Articles

Shared-Memory Parallel Edmonds Blossom Algorithm for Maximum Cardinality Matching in General Graphs.

The Edmonds Blossom algorithm is implemented here using depth-first search, which is intrinsically serial. By streamlining the code, our serial implementation is consistently three to five times faster than the previously fastest general graph matching code. By extracting parallelism across iterations of the algorithm, with coarse-grain locking, we are able to further reduce the run time on random regular graphs four-fold and obtain a two-fold reduction of run time on real-world graphs with similar topology. Solving very sparse graphs (average degree less than four) exhibiting community structure with eight threads led to a slow down of three-fold, but this slow down is replaced by marginal speed up once the average degree is greater than four. We conclude that our parallel coarse-grain locking implementation performs well when extracting parallelism from this augmenting-path-based algorithm and may work well for similar algorithms.

Fractional Matchings in Graphs from the Spectral Radius

Fractional Matchings in Graphs from the Spectral Radius

SEMScene: Semantic-Consistency Enhanced Multi-Level Scene Graph Matching for Image-Text Retrieval

Image-text retrieval, a fundamental cross-modal task, performs similarity reasoning for images and texts. The primary challenge for image-text retrieval is cross-modal semantic heterogeneity, where the semantic features of visual and textual modalities are rich but distinct. Scene graph is an effective representation for images and texts as it explicitly models objects and their relations. Existing scene graph based methods have not fully taken the features regarding various granularities implicit in scene graph into consideration (e.g. triplets), the inadequate feature matching incurs the absence of non-trivial semantic information (e.g. inner relations among triplets). Therefore, we propose a S emantic-Consistency E nhanced M ulti-Level Scene Graph Matching (SEMScene) network, which exploits the semantic relevance between visual and textual scene graphs from fine-grained to coarse-grained. Firstly, under the scene graph representation, we perform feature matching including low-level node matching, mid-level semantic triplet matching, and high-level holistic scene graph matching. Secondly, to enhance the semantic-consistency for object-fused triplets carrying key correlation information, we propose a dual-step constraint mechanism in mid-level matching. Thirdly, to guide the model to learn the semantic-consistency of matched image-text pairs, we devise effective loss functions for each stage of the dual-step constraint. Comprehensive experiments on Flickr30K and MS-COCO datasets demonstrate that SEMScene achieves state-of-the-art performances with significant improvements.

A Theory of Alternating Paths and Blossoms from the Perspective of Minimum Length

The Micali–Vazirani (MV) algorithm for finding a maximum cardinality matching in general graphs, which was published in 1980, remains to this day the most efficient known algorithm for the problem. The current paper gives the first complete and correct proof of this algorithm. The MV algorithm resorts to finding minimum-length augmenting paths. However, such paths fail to satisfy an elementary property, called breadth first search honesty in this paper. In the absence of this property, an exponential time algorithm appears to be called for—just for finding one such path. On the other hand, the MV algorithm accomplishes this and additional tasks in linear time. The saving grace is the various “footholds” offered by the underlying structure, which the algorithm uses in order to perform its key tasks efficiently. The theory expounded in this paper elucidates this rich structure and yields a proof of correctness of the algorithm. It may also be of independent interest as a set of well-knit graph-theoretic facts. Funding: This work was supported in part by the National Science Foundation [Grant CCF-2230414].

Privacy-Preserving Graph Matching Query Supporting Quick Subgraph Extraction

Graph matching, as one of the most fundamental problems in graph database, has a wide range of applications. Due to the large scale of graph database and the hardness of graph matching, it is an attractive alternative to make use of the cloud to store massive data graphs and conduct the complex graph matching. To protect the privacy, data graphs are usually encrypted before being outsourced to the cloud. A few schemes have been proposed to support graph matching query over encrypted graphs. However, none of them can realize efficient subgraph extraction when the matched subgraph needs to be exactly located at the data graph. The graph user has to perform the complex subgraph isomorphism operation to extract the isomorphic subgraph from the matched data graph in state-of-the-art schemes. The time complexity of judging subgraph isomorphism is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(n!n^{2})$</tex-math></inline-formula> at most, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of vertices in the data graph. In order to solve this problem, we propose a privacy-preserving graph matching query scheme supporting quick subgraph extraction in this paper. In our design, two non-colluding cloud servers are adopted to accomplish the matching operation jointly. Neither of them can infer the plaintexts of graphs. The first cloud server can prune some impossible matched vertices from the data graph, and get a possible matched matrix to represent which vertices in the data graph might match with the vertices in the query graph. The second cloud server performs the related matrix operations based on its stored information and the information sent by the first cloud server. The two cloud servers jointly verify the correctness of the matched matrix. The graph user can directly and quickly extract the matrix of the subgraph isomorphic to the query graph from the data graph matrix based on the matched matrix, and further recover this subgraph. No subgraph isomorphism operation is involved in the procedure of subgraph extraction for the graph user. The time complexity of subgraph extraction is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(m^{2})$</tex-math></inline-formula> in our scheme, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> is the number of vertices in the query graph. The extensive experiments with real-world database demonstrate the efficiency of the proposed privacy-preserving graph matching scheme.

3D/2D Vessel Registration Based on Monte Carlo Tree Search and Manifold Regularization.

The augmented intra-operative real-time imaging in vascular interventional surgery, which is generally performed by projecting preoperative computed tomography angiography images onto intraoperative digital subtraction angiography (DSA) images, can compensate for the deficiencies of DSA-based navigation, such as lack of depth information and excessive use of toxic contrast agents. 3D/2D vessel registration is the critical step in image augmentation. A 3D/2D registration method based on vessel graph matching is proposed in this study. For rigid registration, the matching of vessel graphs can be decomposed into continuous states, thus 3D/2D vascular registration is formulated as a search tree problem. The Monte Carlo tree search method is applied to find the optimal vessel matching associated with the highest rigid registration score. For nonrigid registration, we propose a novel vessel deformation model based on manifold regularization. This model incorporates the smoothness constraint of vessel topology into the objective function. Furthermore, we derive simplified gradient formulas that enable fast registration. The proposed technique undergoes evaluation against seven rigid and three nonrigid methods using a variety of data - simulated, algorithmically generated, and manually annotated - across three vascular anatomies: the hepatic artery, coronary artery, and aorta. Our findings show the proposed method's resistance to pose variations, noise, and deformations, outperforming existing methods in terms of registration accuracy and computational efficiency. The proposed method demonstrates average registration errors of 2.14 mm and 0.34 mm for rigid and nonrigid registration, and an average computation time of 0.51 s.

Scalable Diversified Top-k Pattern Matching in Big Graphs

Typically, graph pattern matching is expressed in terms of subgraph isomorphism. Graph simulation and its variants were introduced to reduce the time complexity and obtain more meaningful results in big graphs. Among these models, the matching subgraphs obtained by tight simulation are more compact and topologically closer to the pattern graph than results produced by other approaches. However, the number of resulting subgraphs can be huge, overlapping each other and unequally relaxed from the pattern graph. Hence, we introduce a ranking and diversification method for tight simulation results, which allows the user to obtain the most diversified and relevant matching subgraphs. This approach exploits the weights on edges of the big graph to express the interest of the matching subgraph by tight simulation. Furthermore, we provide distributed scalable algorithms to evaluate the proposed methods based on distributed programming paradigms. The experiments on real data graphs succeed in demonstrating the effectiveness of the proposed models and the efficiency of the associated algorithms. The result diversification reached 123% within a time frame that does not exceed 40%, on average, of the duration required for tight simulation graph pattern matching.

Generalizing Time Aggregation to Out-of-Sample Data Using Minimum Bipartite Graph Matching for Power Systems Studies

Generalizing Time Aggregation to Out-of-Sample Data Using Minimum Bipartite Graph Matching for Power Systems Studies

A Mars Local Terrain Matching Method Based on 3D Point Clouds

To address the matching challenge between the High Resolution Imaging Science Experiment (HiRISE) Digital Elevation Model (DEM) and the Mars Orbiter Laser Altimeter (MOLA) DEM, we propose a terrain matching framework based on the combination of point cloud coarse alignment and fine alignment methods. Firstly, we achieved global coarse localization of the HiRISE DEM through nearest neighbor matching of key Intrinsic Shape Signatures (ISS) points in the Fast Point Feature Histograms (FPFH) feature space. We introduced a graph matching strategy to mitigate gross errors in feature matching, employing a numerical method of non-cooperative game theory to solve the extremal optimization problem under Karush–Kuhn–Tucker (KKT) conditions. Secondly, to handle the substantial resolution disparities between the MOLA DEM and HiRISE DEM, we devised a smoothing weighting method tailored to enhance the Voxelized Generalized Iterative Closest Point (VGICP) approach for fine terrain registration. This involves leveraging the Euclidean distance between distributions to effectively weight loss and covariance, thereby reducing the results’ sensitivity to voxel radius selection. Our experiments show that the proposed algorithm improves the accuracy of terrain registration on the proposed Curiosity landing area’s, Mawrth Vallis, data by nearly 20%, with faster convergence and better algorithm robustness.

Optimal bipartite graph matching-based goal selection for policy-based hindsight learning

The sparse reward problem stands as a significant challenge in the field of reinforcement learning. Hindsight Experience Replay (HER) addresses this by goal relabeling, allowing the agent to learn from unsuccessful experiences. Some studies combine policy gradient methods with HER, resulting in policy-based hindsight learning algorithms. However, Policy-based hindsight learning involves the use of importance sampling, where the distribution of hindsight goals and the distribution of desired goals contribute to the computation of importance weights. When there is a significant difference between the two distributions, importance weights may become skewed, thereby impacting the evaluation of the policy and leading to suboptimal policies. To address this, we propose modeling the goal selection as an optimization problem for distribution matching. After we augment the original desired goals using Kernel Density Estimation (KDE), we further convert the optimization problem for distribution matching into a bipartite graph matching problem that minimizes the sum of weights. Our optimal bipartite graph matching-based hindsight goal selection method can select hindsight goals that are the most closely aligned with the original goals. Experimental results show that algorithms combined with the optimal bipartite graph matching-based hindsight goal selection outperform the original algorithms. Visualizations also demonstrate the superiority of our method in selecting hindsight goals.

Learning symmetry-aware atom mapping in chemical reactions through deep graph matching

Accurate atom mapping, which establishes correspondences between atoms in reactants and products, is a crucial step in analyzing chemical reactions. In this paper, we present a novel end-to-end approach that formulates the atom mapping problem as a deep graph matching task. Our proposed model, AMNet (Atom Matching Network), utilizes molecular graph representations and employs various atom and bond features using graph neural networks to capture the intricate structural characteristics of molecules, ensuring precise atom correspondence predictions. Notably, AMNet incorporates the consideration of molecule symmetry, enhancing accuracy while simultaneously reducing computational complexity. The integration of the Weisfeiler-Lehman isomorphism test for symmetry identification refines the model’s predictions. Furthermore, our model maps the entire atom set in a chemical reaction, offering a comprehensive approach beyond focusing solely on the main molecules in reactions. We evaluated AMNet’s performance on a subset of USPTO reaction datasets, addressing various tasks, including assessing the impact of molecular symmetry identification, understanding the influence of feature selection on AMNet performance, and comparing its performance with the state-of-the-art method. The result reveals an average accuracy of 97.3% on mapped atoms, with 99.7% of reactions correctly mapped when the correct mapped atom is within the top 10 predicted atoms.Scientific contributionThe paper introduces a novel end-to-end deep graph matching model for atom mapping, utilizing molecular graph representations to capture structural characteristics effectively. It enhances accuracy by integrating symmetry detection through the Weisfeiler-Lehman test, reducing the number of possible mappings and improving efficiency. Unlike previous methods, it maps the entire reaction, not just main components, providing a comprehensive view. Additionally, by integrating efficient graph matching techniques, it reduces computational complexity, making atom mapping more feasible.

A constructive Steiner graph matching for Radio frequency identification device tag detection in wireless and internet of things environment

SummaryRadio frequency identification device (RFID) has emerged as one of the most potential building blocks for future IoT‐enabled technologies. Various applications like logistic monitoring use the RFID system to deal with the tagged objects. RFID‐based tracking approach is extremely solicited for appropriate logistic distribution because of the frequent tagged‐objects rearrangements. Nevertheless, with an RFID system, one of the most significant issues is resolving collisions between tags as they transfer data to the reader at the same time. This work investigates the core issue of locating all lost tags in RFID systems. The most significant factor in missing tag recognition is to reduce the time required for execution. A problem needs to be formulated to differentiate the tagged objects' motion state, that is, static or dynamic, to handle this issue. It tracks the moving objects with various existing localization approaches. Finally, a tag detection known as constructive Steiner graph matching (CSGM) detection is proposed to achieve time efficiency by utilizing RFID collision signals. Specifically, the physical‐layer features are considered for differentiating the positions. Experimental outcomes demonstrate that the anticipated model can attain better prediction accuracy by reducing inventory time compared to other approaches. Simulation findings show that the suggested approach performs exceptionally well in giving a significant performance boost in an RFID system. It minimizes the complexity of tracking the objects. The simulation outcomes illustrate that the algorithm's identification speed is substantially enhanced and ensuring high system efficiency. The simulation results of the proposed algorithm have been improved in terms of system efficiency (9.5%), success rate (6.3%), and identification speed (4%) compared to the conventional algorithm. The suggested CSGM technique's average waiting time is decreased by more than 45.372%, and its detection speed is increased by at least 38.219% compared to other existing algorithms.

Robust loop closure detection and relocalization with semantic-line graph matching constraints in indoor environments

Loop closure detection (LCD) plays an essential role in the Simultaneous Localization and Mapping (SLAM) process, effectively reducing cumulative trajectory errors. However, conventional LCD methods often encounter challenges when dealing with variations in illumination, changes in viewpoint, and environments with weak textures. This is due to their reliance on low-level geometric or image features. To address these issues, we propose a robust LCD method named SL-LCD, which integrates semantic information and line features to fully leverage the semantic content and line attributes within indoor scenes, thereby establishing a reliable feature correspondence between query images and loop closure images. For the retrieval of candidate closed-loop images, we construct a semantic-line-segment topological graph and introduce a graph matching algorithm to perform the LCD task. This approach fully exploits image features and spatial information to achieve closed-loop detection in complex indoor scenes. Furthermore, we present a semantic voxel-based generalized ICP (SVGICP) closed-loop relocalization algorithm tailored for challenging and complex indoor scenes, enhancing the accuracy of closed-loop relocalization in such scenarios. Experimental results demonstrate that the SL-LCD algorithm proposed in this paper surpasses state-of-the-art methods, accurately detecting closed loops, and effectively eliminating trajectory drift.

Ensemble Quadratic Assignment Network for Graph Matching

Ensemble Quadratic Assignment Network for Graph Matching

The average size of maximal matchings in graphs

The average size of maximal matchings in graphs

GraphAlign++: An Accurate Feature Alignment by Graph Matching for Multi-Modal 3D Object Detection

GraphAlign++: An Accurate Feature Alignment by Graph Matching for Multi-Modal 3D Object Detection

NExT-OOD: Overcoming Dual Multiple-Choice VQA Biases.

In recent years, multiple-choice Visual Question Answering (VQA) has become topical and achieved remarkable progress. However, most pioneer multiple-choice VQA models are heavily driven by statistical correlations in datasets, which cannot perform well on multimodal understanding and suffer from poor generalization. In this paper, we identify two kinds of spurious correlations, i.e., a Vision-Answer bias (VA bias) and a Question-Answer bias (QA bias). To systematically and scientifically study these biases, we construct a new video question answering (videoQA) benchmark NExT-OOD in OOD setting and propose a graph-based cross-sample method for bias reduction. Specifically, the NExT-OOD is designed to quantify models' generalizability and measure their reasoning ability comprehensively. It contains three sub-datasets including NExT-OOD-VA, NExT-OOD-QA, and NExT-OOD-VQA, which are designed for the VA bias, QA bias, and VA&QA bias, respectively. We evaluate several existing multiple-choice VQA models on our NExT-OOD, and illustrate that their performance degrades significantly compared with the results obtained on the original multiple-choice VQA dataset. Besides, to mitigate the VA bias and QA bias, we explicitly consider the cross-sample information and design a contrastive graph matching loss in our approach, which provides adequate debiasing guidance from the perspective of whole dataset, and encourages the model to focus on multimodal contents instead of spurious statistical regularities. Extensive experimental results illustrate that our method significantly outperforms other bias reduction strategies, demonstrating the effectiveness and generalizability of the proposed approach.

DN-DETR: Accelerate DETR Training by Introducing Query DeNoising.

We present in this paper a novel denoising training method to speed up DETR (DEtection TRansformer) training and offer a deepened understanding of the slow convergence issue of DETR-like methods. We show that the slow convergence results from the instability of bipartite graph matching which causes inconsistent optimization goals in early training stages. To address this issue, except for the Hungarian loss, our method additionally feeds GT bounding boxes with noises into the Transformer decoder and trains the model to reconstruct the original boxes, which effectively reduces the bipartite graph matching difficulty and leads to faster convergence. Our method is universal and can be easily plugged into any DETR-like method by adding dozens of lines of code to achieve a remarkable improvement. As a result, our DN-DETR results in a remarkable improvement ( +1.9AP) under the same setting and achieves 46.0 AP and 49.5 AP trained for 12 and 50 epochs with the ResNet-50 backbone. Compared with the baseline under the same setting, DN-DETR achieves comparable performance with 50% training epochs. We also demonstrate the effectiveness of denoising training in CNN-based detectors (Faster R-CNN), segmentation models (Mask2Former, Mask DINO), and more DETR-based models (DETR, Anchor DETR, Deformable DETR).

Anti-Ramsey number for perfect matchings in 3-regular bipartite graphs

The anti-Ramsey number AR(G,H) is the maximum number of colors in an edge-coloring of a graph in the family G without any rainbow copy of H. The anti-Ramsey number for matchings has been studied extensively in several graph families, while the problem for perfect matchings was only solved in complete graphs. The anti-Ramsey number of matchings in the family of regular bipartite graphs of order large enough was determined by Li and Xu. Jin improved their bounds on the order of 3-regular bipartite graphs. In this paper, we consider the problem for perfect matchings in 3-regular bipartite graphs. Let G be the family of 3-regular bipartite graphs with m vertices in each partite set. First, we characterize the structure of extremal graphs for the Turán number of perfect matchings in graphs with maximum degree three. Using this characterization, we show that AR(G,mK2)=3m−3. Moreover, we show that AR(F,mK2)=3m−5, where F is the subfamily of 3-edge-connected graphs in G. In order to prove this result, we characterize the structure of bipartite graphs, which contains no perfect matchings, with maximum degree three and size Turán number minus one.

Patch-Based Auxiliary Node Classification for Domain Adaptive Object Detection

Domain adaptive object detection (DAOD) aims to leverage labeled source domain data to train object detection models that can generalize well to unlabeled target domains. Recently, many researchers have considered implementing fine-grained pixel-level domain adaptation using graph representations. Existing methods construct semantically complete graphs and align them across domains via graph matching. This work introduced an auxiliary node classification task before domain alignment through graph matching, which utilizes the inherent information of graph nodes to classify them, in order to avoid suboptimal graph matching results caused by node class confusion. However, previous methods neglected the contextual information of graph nodes, leading to biased node classification and suboptimal graph matching. To solve this issue, we propose a novel patch-based auxiliary node classification method for DAOD. Unlike existing methods that use only the inherent information of nodes for node classification, our method exploits the local region information of nodes and employs multi-layer convolutional neural networks to learn the local region feature representation of nodes, enriching the node context information. Thus, accurate and robust node classification results are produced and the risk of class confusion is reduced. Moreover, we propose a progressive strategy to fuse the inherent features and the learned local region features of nodes, which ensures that the network can stably and reliably utilize local region features for accurate node classification. In this paper, we conduct abundant experiments on various DAOD scenarios and demonstrate that our proposed model outperforms existing works.