Weighted 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.

PRISM: Person Reidentification via Structured Matching

Person reidentification (re-id), an emerging problem in visual surveillance, deals with maintaining the identities of individuals while they traverse various locations surveilled by a camera network. Motivated by real-world scenarios, we propose a method that seeks to simultaneously identify who among a group of individuals viewed in one view are present/absent in the other. From a visual perspective, re-id is challenging due to significant changes in visual appearance of individuals in cameras with different pose, illumination, and calibration. Globally, the challenge arises from the need to maintain structurally consistent matches among all the individual entities across different camera views. We propose person re-id via structured matching (PRISM), an SM method to jointly account for these challenges. We view the global problem as a weighted graph matching problem and estimate edge weights by learning to predict them based on the co-occurrences of visual patterns in the training examples. These co-occurrence-based scores in turn account for appearance changes by inferring likely and unlikely visual co-occurrences appearing in training instances. We implement PRISM on single-shot and multishot scenarios. PRISM uniformly outperforms state of the art in terms of matching rate while being robust and computationally efficient.

A dynamical systems approach to weighted graph matching

Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the set of permutations. Contrary to optimization-based relaxations to this problem, in this paper we develop a novel relaxation by constructing dynamical systems on the manifold of orthogonal matrices. In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices. The first minimizes the cost of weighted graph matching over orthogonal matrices, whereas the second minimizes the distance of an orthogonal matrix from the finite set of all permutations. The combination of the two dynamical systems converges to a permutation matrix, which provides a suboptimal solution to the weighted graph matching problem. Finally, our approach is shown to be promising by illustrating it on nontrivial problems.

A Path Following Algorithm for the Graph Matching Problem

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

Graphical Models and Point Pattern Matching

This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.

Large‐scale prediction of disulphide bridges using kernel methods, two‐dimensional recursive neural networks, and weighted graph matching

The formation of disulphide bridges between cysteines plays an important role in protein folding, structure, function, and evolution. Here, we develop new methods for predicting disulphide bridges in proteins. We first build a large curated data set of proteins containing disulphide bridges to extract relevant statistics. We then use kernel methods to predict whether a given protein chain contains intrachain disulphide bridges or not, and recursive neural networks to predict the bonding probabilities of each pair of cysteines in the chain. These probabilities in turn lead to an accurate estimation of the total number of disulphide bridges and to a weighted graph matching problem that can be addressed efficiently to infer the global disulphide bridge connectivity pattern. This approach can be applied both in situations where the bonded state of each cysteine is known, or in ab initio mode where the state is unknown. Furthermore, it can easily cope with chains containing an arbitrary number of disulphide bridges, overcoming one of the major limitations of previous approaches. It can classify individual cysteine residues as bonded or nonbonded with 87% specificity and 89% sensitivity. The estimate for the total number of bridges in each chain is correct 71% of the times, and within one from the true value over 94% of the times. The prediction of the overall disulphide connectivity pattern is exact in about 51% of the chains. In addition to using profiles in the input to leverage evolutionary information, including true (but not predicted) secondary structure and solvent accessibility information yields small but noticeable improvements. Finally, once the system is trained, predictions can be computed rapidly on a proteomic or protein-engineering scale. The disulphide bridge prediction server (DIpro), software, and datasets are available through www.igb.uci.edu/servers/psss.html.

A randomized approach with geometric constraints to fingerprint verification

In this paper, a fuzzy bipartite weighted graph model is proposed to solve fingerprint verification problem. A fingerprint image is preprocessed first to form clusters of feature points, which are called feature point clusters. Twenty-four attributes are extracted for each feature point cluster. The attributes are characterized by fuzzy values. Attributes of an input image to be verified are considered as the set of left nodes in a fuzzy bipartite weighted graph, and the attributes of claimed template fingerprint image are considered as the set of right nodes in the graph. The fingerprint verification problem is thus converted into a fuzzy bipartite weighted graph matching problem. A matching algorithm is proposed for the fuzzy bipartite weighted graph model to find an optimal matching with a goodness score. Experimental results reveal the feasibility of the proposed approach in fingerprint verification.

A linear programming approach for the weighted graph matching problem

A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L/sub 1/ norm and then transforming the resulting quadratic optimization problem to a linear one. The linear program is solved using a simplex-based algorithm. Then, approximate 0-1 integer solutions are obtained by applying the Hungarian method on the real solutions of the linear program. The complexity of the proposed algorithm is polynomial time, and it is O(n/sup 6/L) for matching graphs of size n. The developed algorithm is compared to two other algorithms. One is based on an eigendecomposition approach and the other on a symmetric polynomial transform. Experimental results showed that the LP approach is superior in matching graphs than both other methods. >