Graph Matching Problem Research Articles

An Efficient Service Function Chaining Placement Algorithm in Mobile Edge Computing

Mobile Edge Computing (MEC) is a promising network architecture that pushes network control and mobile computing to the network edge. Recent studies propose to deploy MEC applications in the Network Function Virtualization (NFV) environment. The mobile network service in NFV is deployed as a Service Function Chaining (SFC). In the dynamic and resource-limited mobile network, SFC placement aiming at optimizing resource utilization is a challenging problem. In this article, we solve the SFC placement problem in the MEC-NFV environment. We formulate the SFC placement problem as a weighted graph matching problem, including two sub-problems: a graph matching problem and an SFC mapping problem. To efficiently solve the graph matching problem, we propose a Linear Programming–(LP) based approach to calculate the similarity between VNFs and physical nodes. Based on the similarity, we design a Hungarian-based algorithm to solve the SFC mapping problem. Evaluation results show that our proposed LP-based solutions outperform the heuristic algorithms in terms of execution time and resource utilization.

A scheduling strategy to inter-satellite links assignment in GNSS

By introducing inter-satellite link (ISL), the dependence of the global navigation satellite system (GNSS) on ground infrastructure can be reduced and its performance enhanced via inter-satellite ranging and communication. Owing to platform restrictions, there are usually fewer onboard Ka-band ISL antennas than the number of visible satellites, which poses a problem when optimizing the inter-satellite links assignment of the GNSS. In this study, to optimize inter-satellite ranging and communication, a multi-objective optimization model is built and a scheduling strategy is proposed for the inter-satellite links assignment scheduling problem. The position dilution of precision (PDOP) of links and the transmission time-delay of telemetry data are set as the ranging performance and communication metrics, respectively. We regard the links assignment in each slot as a general graph-matching problem, and apply the Blossom algorithm to obtain the maximum matching. We then generate and optimize the satellite sequences for whole slots using non-dominated sorting genetic algorithm II (NSGA-II). The simulation scenes include 10,080 epochs of GNSS constellation, and the simulation results show that the performance of the proposed strategy is better than that of other methods published recently, and can provide various solutions to meet the different preferences of system managers.

NCC Based Correspondence Problem for First- and Second-Order Graph Matching.

Automatically finding correspondences between object features in images is of main interest for several applications, as object detection and tracking, identification, registration, and many derived tasks. In this paper, we address feature correspondence within the general framework of graph matching optimization and with the principal aim to contribute. We proposed two optimized algorithms: first-order and second-order for graph matching. On the one hand, a first-order normalized cross-correlation (NCC) based graph matching algorithm using entropy and response through Marr wavelets within the scale-interaction method is proposed. First, we proposed a new automatic feature detection processing by using Marr wavelets within the scale-interaction method. Second, feature extraction is executed under the mesh division strategy and entropy algorithm, accompanied by the assessment of the distribution criterion. Image matching is achieved by the nearest neighbor search with normalized cross-correlation similarity measurement to perform coarse matching on feature points set. As to the matching points filtering part, the Random Sample Consensus Algorithm (RANSAC) removes outliers correspondences. One the other hand, a second-order NCC based graph matching algorithm is presented. This algorithm is an integer quadratic programming (IQP) graph matching problem, which is implemented in Matlab. It allows developing and comparing many algorithms based on a common evaluation platform, sharing input data, and a customizable affinity matrix and matching list of candidate solution pairs as input data. Experimental results demonstrate the improvements of these algorithms concerning matching recall and accuracy compared with other algorithms.

Shape correspondence based on Kendall shape space and RAG for 2D animation

We introduce a 2D vectorized shape correspondence method based on Kendall shape space and region adjacency graph. We regard shape correspondence in 2D animation as a weighted bipartite graph matching problem and optimize it by means of various weights, including geometric attribute, local topological information, and global topological information in 2D animation drawing. The measuring method in Kendall shape space is introduced to determine similarity between two regions and a local adjacent region matching method is presented to associate the vicinity of the corresponding region by utilizing local topology information. Ultimately, we propose a globally optimal shape matching method, which exploits the global topological information to get the final result of the shape correspondence. Our approach can efficiently match associated regions that have exaggerated deformation and unstable topology between two shapes in 2D animation. It is also robust to the similarity transformation of shapes.

Resource allocation for virtual reality content sharing based on 5G D2D multicast communication

As the development of wireless virtual reality (VR), a great disparity exists among the huge content transmission, rigorous QoS guarantees and the limited bandwidth of cellular networks. With the increasing of cache capacity on user devices, direct content sharing between user devices is a promising solution to solve this problem. To meet the quality of service (QoS) requirement of wireless VR transmission, this paper proposes a content sharing scheme based on 5G device-to-device (D2D) Multicast Communication. In this way, some adjacent VR users can form multicasting clustering to share VR content by working on D2D communication mode. The VR D2D multicasting clusters reuse the uplink channel resource of ordinary VR cellular users in the same cell. The basic prerequisite is that the degrading on QoS of these ordinary VR cellular users can be affordable. We design a two-step scheme to solve this radio resource allocation problem for VR content sharing. Firstly, we find out the optimal transmitting power for each VR user devices by geometric proximity, which metrics are affected by wireless VR throughput, tracking accuracy and delay. In the second step, we transform the channel allocation problem into a bipartite graph matching problem based on the transmitting power metrics, which is optimally solved by the Hungarian algorithm. The simulation results show that the VR content sharing based on 5G D2D communication technology can achieve larger system throughput gain and lower transmission delay. Compared with heuristic scheme and stochastic scheme, the proposed scheme can increase the throughput of the overall network by about 50% and 12%, respectively.

Fast matching via ergodic markov chain for super-large graphs

In theory, graph matching is a combinatorial problem. One state-of-the-art technique in graph matching, called spectral matching, relaxes the matching problem for consistent correspondence into spectral decomposition of the affinity matrix of graphs, but the most variations of spectral based algorithms suffer from their O(n4) memory requirement. In this paper we propose a probabilistic spectral matching approach, in which the graph matching problem is formulated as an ergodic Markov chain, and the process of matching is addressed to reach the steady-state of the Markov chain. The approach decomposes the probability transition matrix, and solves the matching problem in O(n2) space complexity using limited computing resource and RAM. This property makes the approach suitable for super-large graphs matching (for example, graphs with the number of points over 1000). We evaluate our algorithm on both the synthetic and the real datasets, and demonstrate that the proposed approach is significantly faster, and consumes smaller memory than SM, RRWM and FaSM with no loss of accuracy.

Unifying Offline and Online Multi-Graph Matching via Finding Shortest Paths on Supergraph.

This paper addresses the problem of multiple graph matching (MGM) by considering both offline batch mode and online setting. We explore the concept of cycle-consistency over pairwise matchings and formulate the problem as finding optimal composition path on the supergraph, whose vertices refer to graphs and edge weights denote score function regarding consistency and affinity. By our theoretical study we show that the offline and online MGM on supergraph can be converted to finding all pairwise shortest paths and single-source shortest paths respectively. We adopt the Floyd algorithm [1] and shortest path faster algorithm (SPFA) [2] , [3] to effectively find the optimal path. Extensive experimental results show our methods surpass state-of-the-art MGM methods, including CAO [4] , MISM [5], IMGM [6] , and many other recent methods in offline and online settings. Source code will be made publicly available.

Long-Term Loop Closure Detection through Visual-Spatial Information Preserving Multi-Order Graph Matching

Loop closure detection is a fundamental problem for simultaneous localization and mapping (SLAM) in robotics. Most of the previous methods only consider one type of information, based on either visual appearances or spatial relationships of landmarks. In this paper, we introduce a novel visual-spatial information preserving multi-order graph matching approach for long-term loop closure detection. Our approach constructs a graph representation of a place from an input image to integrate visual-spatial information, including visual appearances of the landmarks and the background environment, as well as the second and third-order spatial relationships between two and three landmarks, respectively. Furthermore, we introduce a new formulation that formulates loop closure detection as a multi-order graph matching problem to compute a similarity score directly from the graph representations of the query and template images, instead of performing conventional vector-based image matching. We evaluate the proposed multi-order graph matching approach based on two public long-term loop closure detection benchmark datasets, including the St. Lucia and CMU-VL datasets. Experimental results have shown that our approach is effective for long-term loop closure detection and it outperforms the previous state-of-the-art methods.

SRA: Secure Reverse Auction for Task Assignment in Spatial Crowdsourcing

In this paper, we study a new type of spatial crowdsourcing, namely competitive detour tasking, where workers can make detours from their original travel paths to perform multiple tasks, and each worker is allowed to compete for preferred tasks by strategically claiming his/her detour costs. The objective is to make suitable task assignment by maximizing the social welfare of crowdsourcing systems and protecting workers’ private sensitive information. We first model the task assignment problem as a reverse auction process. We formalize the winning bid selection of reverse auction as an $n$ n -to-one weighted bipartite graph matching problem with multiple 0-1 knapsack constraints. Since this problem is NP-hard, we design an approximation algorithm to select winning bids and determine corresponding payments. Based on this, a Secure Reverse Auction (SRA) protocol is proposed for this novel spatial crowdsourcing. We analyze the approximation performance of the proposed protocol and prove that it has some desired properties, including truthfulness, individual rationality, computational efficiency, and security. To the best of our knowledge, this is the first theoretically provable secure auction protocol for spatial crowdsourcing systems. In addition, we also conduct extensive simulations on a real trace to verify the performance of the proposed protocol.

Discrete artificial electric field algorithm for high-order graph matching

High-order graph matching is a problem of establishing the correspondences between two sets of visual features subject to high-order matching constraints. This is an NP-hard combinatorial optimization problem and formulated as a maximization problem of matching score over all permutations of features. Artificial electric field algorithm (AEFA) (Yadav et al., 2019) is a proven optimization algorithm in the family of meta-heuristic and performed well for continuous optimization problems. In this article, we extended the AEFA algorithm for combinatorial high-order graph matching problems and introduced a discrete artificial electric field algorithm (DAEFA). This framework incorporates the redefine position and velocity representation scheme, addition–subtraction operation, velocity and position update rules, and a problem specific initialization by using heuristic information. The efficiency of the proposed algorithm is tested over three well-known datasets: synthetic, CMU house and real-world datasets. The computational results measured the matching score, accuracy of matching and established the correspondences between two graphs. The computational results show the outperformance of the proposed algorithm over the other state-of-art algorithms in terms of good matching score and accuracy both.

Enabling Security-Aware D2D Spectrum Resource Sharing for Connected Autonomous Vehicles

With the emergence of automated driving technology, wireless demand for secure information exchange among automated vehicles has increased dramatically. To this end, we design a security-aware dynamic device-to-device (D2D) spectrum resource sharing mechanism to enhance the security of vehicular D2D communications with the improved spectrum efficiency. Considering both resource block (RB) sharing and power control, we model this joint D2D spectrum resource sharing process as a weighted bipartite graph matching problem whose weights are obtained through deriving the closed-form solutions of power control in an algebraic method. Then, the global optimal solutions of the matching problem are obtained by using the Hungarian algorithm. Furthermore, a security-aware RB and power allocation (SA-RBPA) mechanism compatible with existing cellular networks is proposed for the small cell base station applications. Extensive simulation results have shown that, compared with existing approaches that consider RB reusing strategy or power control scheme optimization alone, the SA-RBPA scheme is able to realize a better spectrum efficiency and security performance.

Reducing Invertible Embedding Distortion Using Graph Matching Model

Invertible embedding allows the original cover and embedded data to be perfectly reconstructed. Conventional methods use a well-designed predictor and fully exploit the carrier characteristics. Due to the diversity, it is actually hard to accurately model arbitrary covers, which limits the practical use of methods relying heavily on content characteristics. It has motivated us to revisit invertible embedding operations and propose a general graph matching model to generalize them and further reduce the embedding distortion. In the model, the rate-distortion optimization task of invertible embedding is derived as a weighted bipartite graph matching problem. In the bipartite graph, the nodes represent the values of cover elements, and the edges indicate the candidate modifications. Each edge is associated with a weight indicating the corresponding embedding distortion for the connected nodes. By solving the minimum weight maximum matching problem, we can find the optimal embedding strategy under the constraint. Since the proposed work is a general model, it can be incorporated into existing works to improve their performance, or used for designing new invertible embedding systems. We incorporate the proposed work into a part of state-of-the-arts, and experiments show that it significantly improves the rate-distortion performance. To the best knowledge of the authors, it is probably the first work studying rate-distortion optimization of invertible embedding from the perspective of graph matching model.

The maximum 1-2 matching problem and two kinds of its variants

We present an algorithm for solving the maximum 1-2 matching problem in bipartite graphs by reducing it to solving the 1-1 matching in general undirected graphs. Further, we propose two variants of the maximum 1-2 matching problem: one is the maximum 1-2 matching problem of the different kind in divided bipartite graphs and the other is the maximum 1-2 matching problem of the same kind in divided bipartite graphs. The former one is shown to be solved by a similar algorithm to that of the maximum 1-2 matching problem by reducing it to solve the maximum 1-1 matching problem in bipartite graphs. For the latter one, we can only present the augmenting subgraph theorem, which is an extension of our augmenting trail theorem for the maximum 1-2 matching problem.

A method for feature matching in images using descriptor structures

A method of feature matching in images using descriptor structures is considered in the work. The descriptors in the developed method can be any known solutions in the field of computer vision. However, inaccuracies can occur when matching image pairs. It is proposed that descriptor structures should be compared to eliminate the “outliers”. Descriptor structures are described using graphs. An Umeyama method is used to find matching features using descriptor structures. The method is based on the decomposition of matrices into eigenvalues and eigenvectors for weighted graph matching problems. Thus, matches are based on the descriptor at the initial stage. Two graphs are then constructed for each image based on the resulting sets of mapped features. The weights of the graph are distances between all image features, calculated using the Gauss function. Weight matrices are built for each graph. Matrix decomposition is carried out into eigenvalues and eigenvectors. The resulting matrix is calculated based on the Umeyama method and correct matches are found. Thus, false matches are excluded from the set of matches obtained using descriptors by comparing structures. The method is invariant to zoom and in-plane image rotation. The method leads to correct results only if the number of correct matches is greater than the number of false matches. The complexity of the developed algorithm is proportional to the number of matches found.

Hypergraph isomorphism using association hypergraphs

Association graphs represent a classical tool to deal with the graph matching problem and recently the idea has been generalized to the case of hypergraphs. In this article, the potential of this approach is explored. The proposed framework uses a class of dynamical systems derived from the Baum-Eagon inequality in order to find the maximum (maximal) clique in the association hypergraph, that corresponds to the maximum (maximal) isomorphism between the hypergraphs to be matched. The proposed approach has extensively been tested with experiments on a large synthetic dataset, including hypergraphs of different cardinalities, order and connectivities. In particular the isomorphism version of the problem has been analyzed. The results obtained are impressive in terms of correctness, thus showing that, despite its simplicity, the Baum-Eagon dynamics has an outstanding capacity of finding globally optimal solutions and solving the hypergraph isomorphism problem.

Image Correspondence With CUR Decomposition-Based Graph Completion and Matching

Establishing correspondence between pictorial descriptions of two images is an important task and can be treated as graph matching problem. However, the process of extracting a favourable graph structure from raw images for matching is influenced by cluttered backgrounds and deformations, which may result in the abundance of noisy graph structures. This paper addresses the problem of point set correspondence and presents a robust graph matching method which recovers the correspondence matches among the graph nodes in a CUR based factorization framework. The graph representation in terms of CUR, inherently preserves the actual nodes connection in sparse manner, this particularly renders the complex space-time realization of affinities among graph nodes. The reformulation of graph matching in terms of small CUR factorization matrices, allows to compute and relax the partially observed graphs, without observing the whole large-scale graph matrix. In particular, we propose two variants of this approach, first, approximating the matching matrix from small CUR observed graph structure, and second, completing the graph structure with higher order CUR form to find correspondence. The CUR based matching algorithms are realized by computing set of compatibility coefficients from pairwise matching graphs and further conducting the probability relaxation procedure to find the matching confidences among nodes. Experiments and analysis on synthetic and natural images dataset prove the effectiveness of proposed methods against state-of-the-art methods. We also explore CUR matching for non-rigid moving object in a video sequence to demonstrate the potential application of graph matching to video analysis.

An efficient algorithm for bounded spectral matching with affine constraint

SummaryGraph matching problem appears frequently in the applications of computer vision and machine learning. In this work, based on the spectral matching with affine constraint (SMAC) formulation, we present a new formulation, named bounded SMAC (BSMAC), for the graph matching problem by adding an upper‐bound constraint on the solution norm. We demonstrate the existence of a unique solution with BSMAC, whereas SMAC needs not to have any meaningful solution in general. We develop an effective numerical method to solve the BSMAC formulation as an optimization problem. Numerical experiments are presented to verify feasibility and to show the performance of the proposed numerical method.

Finding the polygon hull of a network without conditions on the starting vertex

AbstractMany real‐life problems arising within the fields of wireless communication, image processing, combinatorial optimization, etc, can be modeled by means of Euclidean graphs. In the case of wireless sensor networks, the overall topology of the graph is not known because sensor nodes are often randomly deployed. One of the significant problems in this field is the search for boundary nodes. This problem is important in cases such as the surveillance of an area of interest, image contour reconstruction, graph matching problems, routing or clustering data, etc. In the literature, many algorithms are proposed to solve this problem, a recent one of which is the least polar‐angle connected node (LPCN) algorithm and its distributed version D‐LPCN, which are both based on the concept of a polar angle visit. An inconvenience of these algorithms is the determination of the starting vertex. In effect, the point with the minimum x‐coordinate is a possible starting point, but it has to be known at the beginning, which considerably increases the algorithms' complexity. In this article, we propose a new method called RRLPCN (reset and restart with least polar‐angle connected node), which is based on the LPCN algorithm to find the boundary vertices of a Euclidean graph. The main idea is to start the LPCN algorithm from an arbitrary vertex, and whenever it finds a vertex with an x‐coordinate smaller than that of the starting one, LPCN is reset and restarted from this new vertex. The algorithm stops as soon as it visits the same edge for the second time in the same direction. In addition to finding the boundary vertices, RRLPCN also finds the vertex with minimum x‐coordinate, which is the last starting point of our algorithm. The distributed version of the proposed algorithm, called D‐RRLPCN, is then applied to boundary node detection in the wireless sensor network. It has been implemented using real sensor nodes (Arduino/XBee and TelosB). The simulation results have shown our algorithm to be very effective in comparison to other algorithms.

An Efficient Approach for Graph-Based Fault Diagnosis in UAVs

In this work, we tackle the problem of systematic population of a bank of residual generators for model-based fault diagnosis in Unmanned Aerial Vehicles (UAVs). Intended for detailed, large and non-linear system models, Structural Analysis (SA) is applied to produce a graph-based abstraction of the problem in the form of a bipartite graph. The Branch and Bound Integer Linear Programming (BBILP) algorithm is employed, properly adapted to seek a solution for the constrained graph matching problem. Appropriate causality constraints are formulated, which link the structure of the system graph with the analytical form of the residual generators and certify that all resulting residual generators can be implemented automatically using numerical processes. An extensive performance investigation of the proposed approach is carried out, which is shown to be more efficient than other similar algorithms. Benchmarks of UAV models taken from the literature are presented and a simulated response of the diagnostic system against a fault in the roll-rate sensor is showcased.

Pose-Based Composition Improvement for Portrait Photographs

This paper studies the composition in portrait paintings and develops an algorithm to improve the composition of portrait photographs based on example portrait paintings. A study of portrait paintings shows that the placement of the face and the figure is pose-related. Based on this observation, this paper develops an algorithm to improve the composition of a portrait photograph by learning the placement of the face and the figure from an example portrait painting. This example portrait painting is selected based on the similarity of its figure pose to that of the input photograph. This similarity measure is modeled as a graph matching problem. Finally, space cropping is performed using an optimization function to assign a similar location for each body part of the figure in the photograph with that of the figure in the example portrait painting. The experimental results demonstrate the effectiveness of the proposed method. A user study shows that the proposed pose-based composition improvement is preferred more than rule-based methods and learning-based methods.