Graph Edit Distance Problem Research Articles

A Secure Multi-Party Computation Protocol for Graph Editing Distance against Malicious Attacks

The secure computation of the graph structure is an important element in the field of secure calculation of graphs, which is important in querying data in graphs, since there are no algorithms for the graph edit distance problem that can resist attacks by malicious adversaries. In this paper, for the problem of secure computation of similarity edit distance of graphs, firstly, the encoding method applicable to the Paillier encryption algorithm is proposed, and the XOR operation scheme is proposed according to the Paillier homomorphic encryption algorithm. Then, the security algorithm under the semi-honest model is designed, which adopts the new encoding method and the XOR operation scheme. Finally, for the malicious behaviors that may be implemented by malicious participants in the semi-honest algorithm, using the hash function, a algorithm for secure computation of graph editing distance under the malicious model is designed, and the security of the algorithm is proved, and the computational complexity and the communication complexity of the algorithm are analyzed, which is more efficient compared with the existing schemes, and has practical value. The algorithm designed in this paper fills the research gap in the existing literature on the problem of graph edit distance and contributes to solving the problem.

Computing Graph Edit Distance via Neural Graph Matching

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%.

Efficient parallel branch-and-bound approaches for exact graph edit distance problem

Graph Edit Distance (GED) is a well-known measure used in the graph matching to measure the similarity/dissimilarity between two graphs by computing the minimum cost of edit operations needed to transform one graph into another. This process, Which appears to be simple, is known NP-hard and time consuming since the search space is increasing exponentially. One way to optimally solve this problem is by using Branch and Bound (B&B) algorithms, Which reduce the computation time required to explore the whole search space by performing an implicit enumeration of the search space instead of an exhaustive one based on a pruning technique. nevertheless, They remain inefficient when dealing with large problem instances due to the impractical running time needed to explore the whole search space. To overcome this issue, We propose in this paper three parallel B&B approaches based on shared memory to exploit the multi-core CPU processors: First, a work-stealing approach where several instances of the B&B algorithm explore a single search tree concurrently achieving speedups up to 24× faster than the sequential version. Second, a tree-based approach where multiple parts of the search tree are explored simultaneously by independent B&B instances achieving speedups up to 28×. Finally, Due to the irregular nature of the GED problem, two load-balancing strategies are proposed to ensure a fair workload between parallel processes achieving impressive speedups up to 300×. all experiments have been carried out on well-known datasets

Computing graph edit distance on quantum devices

Distance measures provide the foundation for many popular algorithms in Machine Learning and Pattern Recognition. Different notions of distance can be used depending on the types of the data the algorithm is working on. For graph-shaped data, an important notion is the Graph Edit Distance (GED) that measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. As the complexity of computing GED is the same as NP-hard problems, it is reasonable to consider approximate solutions. In this paper, we present a QUBO formulation of the GED problem. This allows us to implement two different approaches, namely quantum annealing and variational quantum algorithms, that run on the two types of quantum hardware currently available: quantum annealer and gate-based quantum computer, respectively. Considering the current state of noisy intermediate-scale quantum computers, we base our study on proof-of-principle tests of their performance.

Efficient approximate approach for graph edit distance problem

• Near optimal results, with a less than 5% deviation from optimal results of a DFS algorithm. • Fast execution time. • Scalable since it can deal with large data-sets in small execution time. • report tight upper-bounds for large data-sets. Graph Edit Distance (GED) problem is a well-known tool used to measure the similarity/dissimilarity between two graphs. It searches for the best set of edit operations (in terms of cost) that transforms one graph into another. Due to the NP-hardness nature of the problem, the search space increases exponentially making exact approaches impossible to use for large graphs. In this context, there is a huge need for approaches that give near-optimal results in reasonable time. In this paper, we propose a tree-based approximate approach for dealing with GED problem. It operates on a search tree that models all possible solutions of the problem. Since exploring the whole tree is impractical; this approach keeps only the best k nodes at each level of the tree for further exploration. This reduces enormously the execution time without scarifying the solution quality. Experiments using small and medium size data-sets show the low deviation of our results as compared to the optimal results of a Depth First Search algorithm. Moreover, our approach show a strong scalability potential by dealing with large data-sets in low execution time.

Approximate Graph Edit Distance in Quadratic Time.

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently, the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation, we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

Learning edit cost estimation models for graph edit distance

One of the most popular distance measures between a pair of graphs is the Graph Edit Distance. This approach consists of finding a set of edit operations that completely transforms a graph into another. Edit costs are introduced in order to penalize the distortion that each edit operation introduces. Then, one basic requirement when we design a Graph Edit Distance algorithm, is to define the appropriate edit cost functions. On the other hand, Machine Learning algorithms has been applied in many contexts showing impressive results, due, among other things, its ability to find correlations between input and output values. The aim of this paper is to bring the potentialities of Machine Learning to the Graph Edit Distance problem presenting a general framework in which this kind of algorithms are used to estimate the edit costs values for node substitutions.

Graph edit distance: Accuracy of local branching from an application point of view

In the context of graph-based representations, comparing and measuring the dissimilarities between graphs can be done by solving the Graph Edit Distance (GED) problem. It is well known and embedded in many application fields such as Computer Vision and Cheminformatics. GED is a NP-hard minimization problem, therefore the optimal solution cannot be found in reasonable time. The GED problem has been addressed by exact approaches like Mixed Integer Linear Programs (MILP) formulations and heuristic approaches like beam-search, bipartite graph matching among others. Recently, a novel heuristic, called local branching (LocBra) for the GED problem, has been proposed and shown to be efficient. In this work, the focus is on evaluating LocBra with other competitive heuristics available in the literature from an application point of view. Moreover, it tries to answer the following question: is it important to compute an accurate GED regarding the final applications? Similarity search and graph matching are considered as final applications. Three experiments are conducted to evaluate the accuracy and efficiency of the heuristics. The quality of the obtained solutions and matching w.r.t. optimal solutions and ground-truth matching is studied. The results of those experiments show that LocBra has a high correlation with the optimal solutions and the ground-truth matching.

A local branching heuristic for solving a Graph Edit Distance Problem

The Graph Edit Distance (GED) problem is a very interesting problem that relates to Graph Matching (GM) problems, wherever a graph models a problem-defined pattern. Solving the GED problem leads to compute the matching between two given graphs by minimizing their GED, which is also called a dissimilarity measure between them. It has many application domains such as structural pattern recognition and chemical Structure-Activity Relationships (SAR). GEDEnA (Edges no Attributes) is a sub-problem of the GED problem that deals with a special type of graphs where edges do not carry attributes. They are both NP-hard problems and it is difficult to find the optimal solution in reasonable time. Many heuristics exist in the literature that give suboptimal solutions. Some other works have used mathematical programming tools to model and solve these two problems. The present work takes advantage of a powerful Mixed Integer Linear Program (MILP) formulation and proposes a heuristic called Local Branching to solve the GEDEnA problem. Mainly, a MILP model is iteratively modified by adding additional constraints to define neighborhoods in the solution space, which are explored using a black-box solver. A problem-dependent exploration is performed to find efficient solutions. Lastly, the proposed heuristic is evaluated considering two factors: its computational time and solution quality against the heuristics available in the literature and exact methods. The computational experiments reported in this paper show that the proposed local branching heuristic strongly outperforms the existing heuristics for the GEDEnA problem.

A parallel graph edit distance algorithm

Graph edit distance (GED) has emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning, and data mining. GED is an error-tolerant graph matching problem which consists in minimizing the cost of the sequence that transforms a graph into another by means of edit operations. Edit operations are deletion, insertion and substitution of vertices and edges. Each vertex/edge operation has its associated cost defined in the vertex/edge cost function. Unfortunately, Unfortunately, the GED problem is NP-hard. The question of elaborating fast and precise algorithms is of first interest. In this paper, a parallel algorithm for exact GED computation is proposed. Our proposal is based on a branch-and-bound algorithm coupled with a load balancing strategy. Parallel threads run a branch-and-bound algorithm to explore the solution space and to discard misleading partial solutions. In the mean time, the load balancing scheme ensures that no thread remains idle. Experiments on 4 publicly available datasets empirically demonstrated that under time constraints our proposal can drastically improve a sequential approach and a naive parallel approach. Our proposal was compared to 6 other methods and provided more precise solutions while requiring a low memory usage.

Improving bipartite graph edit distance approximation using various search strategies

Recently the authors of the present paper introduced an approximation framework for the graph edit distance problem. The basic idea of this approximation is to first build a square cost matrix C=(cij), where each entry cij reflects the cost of a node substitution, deletion or insertion plus the matching cost arising from the local edge structure. Based on C an optimal assignment of the nodes and their local structure can be established in polynomial time. Since this approach considers local – rather than the global – structural properties of the graphs only, the graph edit distance derived from the optimal node assignment generally overestimates the true edit distance. The present paper pursues the idea of applying additional search strategies that build upon the initial assignment in order to reduce this overestimation. To this end, six different search strategies are investigated in this paper. In an exhaustive experimental evaluation on five real world graph data sets we empirically verify a substantial gain of distance accuracy by means of all search methods while run time remains remarkably low.