Graph Edit Distance

Many tasks in computer vision and pattern recognition are formulated as graph matching problems. Despite the NP-hard nature of the problem, fast and accurate approximations have led to significant progress in a wide range of applications. Learning graph matching functions from observed data, however, still remains a challenging issue. This paper presents an effective scheme to parametrize a graph model for object matching in a classification context. For this, we propose a representation based on a parametrized model graph, and optimize it to increase a classification rate. Experimental evaluations on real datasets demonstrate the effectiveness (in terms of accuracy and speed) of our approach against graph classification with hand-crafted cost functions.

Three research problems are addressed in this study. The first one is a semi-supervised clustering problem with instance-level constraints where each data object is either a closed convex bounded polytope or a closed disk. We first model the problem of computing the centroid of a given cluster as a second order cone programming problem. Also, a subgradient algorithm is adopted for its faster solution. We then propose a mixed-integer second order cone programming formulation and six heuristic approaches for the considered clustering problem. Finally, we compare solution approaches in terms of computational time and quality on randomly generated and real life datasets. The second problem deals with mining a single graph to find central group of nodes of the graph. For the identification of central nodes, we utilize the group betweenness centrality (GBC) measure. We propose a method that first computes upper and lower bounds on the GBC of several groups. The method then eliminates grou...

In data mining systems, which operate on complex data with structural relationships, graphs are often used to represent the basic objects under study. Yet, the high representational power of graphs is also accompanied by an increased complexity of the associated algorithms. Exact graph similarity or distance, for instance, can be computed in exponential time only. Recently, an algorithmic framework that allows graph dissimilarity computation in cubic time with respect to the number of nodes has been presented. This fast computation is at the expense, however, of generally overestimating the true distance. The present paper introduces six different post-processing algorithms that can be integrated in this suboptimal graph distance framework. These novel extensions aim at improving the overall distance quality while keeping the low computation time of the approximation. An experimental evaluation clearly shows that the proposed heuristics substantially reduce the overestimation in the existing approximation framework while the computation time remains remarkably low.

Extract the features for a multi-touch gesture is difficult due to the complex temporal and motion relations between multiple trajectories. In this paper we present a new generic graph model to quantify the shape, temporal and motion information from multi-touch gesture. To make a comparison between graph, we also propose a specific graph matching method based on graph edit distance. Results prove that our graph model can be fruitfully used for multi-touch gesture pattern recognition purpose with the classifier of graph embedding and SVM.

In the recent years, Graph Edit Distance has awaken interest in the scientific community and some new graph-matching algorithms that compute it have been presented. Nevertheless, these algorithms usually cannot be used in real applications due to runtime restrictions. For this reason, other graph-matching algorithms have also been used that compute an approximation of the graph correspondence with lower runtime. Clearly, in a real application, there is a tradeoff between runtime and accuracy. One of the most costly part in these algorithms is the deduction of the node-to-node mapping. We present a new graph-matching algorithm that returns a graph correspondence without the explicit computation of the assignment problem. This is done thanks to a classification of the node-to-node assignment learned in a previous training stage.

This paper presents a preliminary research work for the analysis of handwritten arithmetic operations in the context of e-education. Given a mathematical exercise, an answer in the form of an arithmetical operation is expected from a child. This answer can be represented by a graph containing both expected numbers and their corresponding relationship one to another. We propose to compute several hypotheses Fuzzy Visibility Graph of symbols over a child's input. The widely used A* algorithm to compute exact graph edit distance is applied over those graphs to match the expected answer. To reduce the search complexity, simplified graphs of operands are first generated and used. Each operand is a sub-graph of the original graph, the algorithm is then applied on the pairs of matched sub-graphs. The hypothesis graph with the smallest graph edit distance with the expected graph and the matched differences can be used to produce an adapted feedback. The result of an experiment over a given example is presented.

Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not been investigated adequately yet. The intergraph node similarity is important in learning a new graph based on the knowledge of an existing graph (transfer learning in graphs) and has applications in biological, communication, and social networks. In this paper, we propose a novel distance function for measuring inter-graph node similarity with edit distance, called NED. In NED, two inter-graph nodes are compared according to their local neighborhood topological structures which are unlabeled unordered k-adjacent trees. Since the computation problem of tree edit distance on unordered trees is NP-Complete. In this paper, we propose a modified tree edit distance, called TED* for comparing neighborhood trees. The TED* is also a metric distance as the original tree edit distance but more importantly, TED* is polynomially computable. Compared to existing inter-graph node similarity measures, not only NED is a metric for nodes that can admit efficient indexing methods, but also by using topological information, NED is a more precise measure for real-world applications such as graph de-anonymization. The efficiency and effectiveness of NED are empirically demonstrated by using real-world graphs.

We model the edit distance as a function in a labelling space. A labelling space is an Euclidean space where coordinates are the edit costs. Through this model, we define a class of cost. A class of cost is a region in the labelling space that all the edit costs have the same optimal labelling. Moreover, we characterise the distance value through the labelling space. This new point of view of the edit distance gives as the opportunity of defining some interesting properties that are useful for a better understanding of the edit distance. Finally, we show the usefulness of these properties through some applications.

In the recent years, Graph Edit Distance has awaken interest in the scientific community and some new graph-matching algorithms that compute it have been presented. Nevertheless, these algorithms usually cannot be used in real applications due to runtime restrictions. For this reason, other graph-matching algorithms have also been used that compute an approximation of the graph correspondence with lower runtime. Clearly, in a real application, there is a tradeoff between runtime and accuracy. One of the most costly part in these algorithms is the deduction of the node-to-node mapping. We present a new graph-matching algorithm that returns a graph correspondence without the explicit computation of the assignment problem. This is done thanks to a classification of the node-to-node assignment learned in a previous training stage.

In agriculture, the soil properties influence the productivity and quality of crops. The farmer expects that in a specific area of the land, the physicochemical characteristics of the soil will be homogeneous as the selected crop has the desired quality and minimizes the use of fertilizers. There are three approaches to determining the correct delimitation of the land in the state-of-the art. The first one (k-means and fuzzy k-means) is impractical for current agricultural technology. The second approach is based on integer linear programming and a pre-processing step. This approach limits the shapes of delimited zones to rectangular, and the third approach extends the solution search space and generates orthogonal regions using Estimation of Distribution Algorithms (EDA). In this work, we generate orthogonal regions with a different approach to the EDA, a greedy construction heuristic. Our heuristic produces feasible solutions with a reasonable running time compared with the runnin...

When several subjects solve the assignment problem of two sets, differences on the correspondences computed by these subjects may occur. These differences appear due to several factors. For example, one of the subjects may give more importance to some of the elements' attributes than another subject. Another factor could be that the assignment problem is computed through a suboptimal algorithm and different non-optimal correspondences can appear. In this paper, we present a consensus methodology to deduct the consensus of several correspondences between two sets. Moreover, we also present an online learning algorithm to deduct some weights that gauge the impact of each initial correspondence on the consensus. In the experimental section, we show the evolution of these parameters together with the evolution of the consensus accuracy. We observe that there is a clear dependence of the learned weights with respect to the quality of the initial correspondences. Moreover, we also observe that in the first iterations of the learning algorithm, the consensus accuracy drastically increases and then stabilises.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  Sub-optimal computation of Graph Edit Distance.  Error-tolerant algorithms: Fast Bipartite and Hausdorff Edit Distance.  Analysis of 8 different local sub-structures.  Recognition ratio and runtime comparison.

This paper is based on a research project aiming at improving learning arithmetic operations at school using penbased tablets. Given an arithmetic operation instruction, the goal is to analyze a child's handwritten answer. This comes down to find if any mistakes are made and their nature. An adapted representation and similarity search are needed for this analysis. In this paper, we propose to use a valued graph representation for handwritten arithmetical operations. To produce the analysis, we compute a similarity search with the corresponding expected answer using Graph Edit Distance (GED). To make up for the uncertainty of the noisy handwritten input recognition, we produce several segmented graph hypotheses for a single answer. Using the GED, we are able to correlate each hypothesis to the instruction graph. It enables to highlight multiple kinds of mistakes a child can make. The GED computation being a NPcomplete problem, we propose to use sub-graph isomorphism: we partially match the instruction on each hypothesis in polynomial time to cut part of the tree search. Experiments were conducted on an in-house dataset composed of 400 handwritten arithmetical additions written by children on pen-based tablet. The time required for the GED computation is evaluated. We are able to match the complete operation in reasonable time on larger graphs while finding most of the time the best corresponding hypothesis.

This paper is based on a research project aiming at improving learning long arithmetic operations in primary school using pen-based tablets. The goal is to automatically analyze a student's handwritten answer by comparing it to an expected answer and to provide immediate feedback. This comes down to find any mistake made such as a calculus mistake, missing carry over or symbol misalignment. We use the correspondence obtained by the Graph Edit Distance (GED) computed between both the student and expected answers. In order to reduce graph sizes to overcome the computational complexity of the GED on large graphs, we present a new semantic graph of line segmentation. We propose a backtracking process to correct potential early mis-recognition mistakes for non-corresponding vertices. We evaluate the improvement on the analysis performances for an increasing number of backtracks on an in-house dataset composed of 400 handwritten operations.

This paper presents a preliminary research work for the analysis of handwritten arithmetic operations in the context of e-education. Given a mathematical exercise, an answer in the form of an arithmetical operation is expected from a child. This answer can be represented by a graph containing both expected numbers and their corresponding relationship one to another. We propose to compute several hypotheses Fuzzy Visibility Graph of symbols over a child's input. The widely used A* algorithm to compute exact graph edit distance is applied over those graphs to match the expected answer. To reduce the search complexity, simplified graphs of operands are first generated and used. Each operand is a sub-graph of the original graph, the algorithm is then applied on the pairs of matched sub-graphs. The hypothesis graph with the smallest graph edit distance with the expected graph and the matched differences can be used to produce an adapted feedback. The result of an experiment over a gi...

Supérieure (a) graph matching without learning (b) with a learned matching function (c) a learned graph model and its matching Figure 1: Graph learning for matching. Our approach learns a graph model from labeled data to provide the best match to instances of a target class. It shows significant improvement over previous approaches for matching.

In graph matching, Graph Edit Distance (GED) is a wellknown distance measure for graphs and it is a NP-Hard minimization problem. Many heuristics are defined in the literature to give approximated solutions in a reasonable time. Some other work have used mathematical programming tools to come up with Mixed Integer Linear Program (MILP) models. In this work, a heuristic from Operational Research domain, is proposed and adapted to handle GED problem. It is called Local Branching and operates over a MILP model, where it defines neighborhoods in the solution space by adding the local branching constraint. A black-box MILP solver is then used to intensify the search in a neighborhood. This makes the solution search very fast, and allow exploring different sub-regions. Also, it includes a diversification mechanism to escape local solutions and in this work this mechanism is modified and improved. Finally, it is evaluated against other heuristics in order to show its efficiency and precision.

In the recent years, Graph Edit Distance has awaken interest in the scientific community and some new graph-matching algorithms that compute it have been presented. Nevertheless, these algorithms usually cannot be used in real applications due to runtime restrictions. For this reason, other graph-matching algorithms have also been used that compute an approximation of the graph correspondence with lower runtime. Clearly, in a real application, there is a tradeoff between runtime and accuracy. One of the most costly part in these algorithms is the deduction of the node-to-node mapping. We present a new graph-matching algorithm that returns a graph correspondence without the explicit computation of the assignment problem. This is done thanks to a classification of the node-to-node assignment learned in a previous training stage.

Many tasks in computer vision and pattern recognition are formulated as graph matching problems. Despite the NP-hard nature of the problem, fast and accurate approximations have led to significant progress in a wide range of applications. Learning graph matching functions from observed data, however, still remains a challenging issue. This paper presents an effective scheme to parametrize a graph model for object matching in a classification context. For this, we propose a representation based on a parametrized model graph, and optimize it to increase a classification rate. Experimental evaluations on real datasets demonstrate the effectiveness (in terms of accuracy and speed) of our approach against graph classification with hand-crafted cost functions.

In this dissertation it is argued that techniques rooted in the theory and practice of programming languages, language based techniques if you will, constitute a strong basis for the investigation of models of biological systems as formalised in a process calculus. In particular it is argued that Static Program Analysis provides a useful approach to the study of qualitative properties of such models. In support of this claim a number of static program analyses are developed for Regev’s BioAmbients – a bio-inspired variant of Cardelli’s Ambient Calculus that incorporates all features of Milner’s π-alculus.

An important role of intelligence organizations is to be able to identity and predict threats within a vast quantity of imprecise and noisy information. We describe the concept and function of our pattern-matching architecture, LAW (Link Analysis Workbench). This system is based upon two main ideas. The first idea is that both the data and the threats can be described in term of graphs of entities and events linked together with semantic relationships. Therefore, graph-based pattern matching techniques can be used to identify threats. The second idea is that analysts constitute an essential part of the system; LAW is designed to handle a lot of interaction with the user, particularly to help in authoring and revising patterns, by allowing analysts to understand the matching process and results.

Perkembangan teknologi dizaman yang modern ini membuat manusia ingin segalanya effesien dan praktis. Mulai dari bahan pangan, sandang, dan papan serta teknologi yang seiring semakin pesat yang mempermudah masyarakat. Namun berdasarkan data-data yang akurat bahwa kejahatan bermodus pencurian kendaraan yang semakin meningkat disetiap tahunnya, maka peneliti mengemukakan ide untuk merancang bangun aplikasi scanner car location untuk meminimalisir kejahatan pencurian kendaraan. Aplikasi scanner car location ini dirancang menggunakan algoritma dijkstra dengan metode waterfall. Rangka dasar dari aplikasi ini adalah aplikasi scanner car location berbasis android yang mempunyai aplikasi tersebut telah dilengkapi scanner Qr-code yang berisi titik lokasi Global Positioning System (GPS) tracker yang telah dipasang pada kendaraan, sehingga ketika saat di scan dapat terlacak keberadaan kendaraan tersebut. Setelah Aplikasi ini terbuat, akan diimplementasikan dan dievaluasi serta akan dimaintenanc...

Pengembangan e-commerce memungkinkan sebuah bisnis berlangsung secara daring baik itu untuk kegiatan penjualan, pembelian, ataupun pemasaran. E-commerce mempu menyediakan informasi yang paling terkini mengenai produk atau jasa yang disediakan. Pembatasan Sosial Berskala Besar (PSBB) dalam rangka mencegah penyebaran virus covid-19 mengakibatkan penurunan daya beli masyarakat. Hal ini langsung berdampak pada pelaku usaha, salah satunya adalah toko Loro Blonyo, toko ini merupakan usaha kecil yang bergerak dalam bidang penjualan dan pemasaran pakaian dan kerajinan batik. Diperlukan model e-commerce berbasis web untuk mengatasi permasalahan pada toko Loro Blonyo, mengingat pada saat ini telah terjadi pergeseran pola atau kebiasaan masyarakat dalam berbelanja dari offline ke online. Model e-commerce berbasis web dikembangkan dengan menggunakan CMS dan BMS. CMS digunakan untuk mengembangkan mode e-commerce berbasis web dan BMS digunakan untuk menganalisis sistem berjalan dan mengidentifika...

T HIS poster shows that arbitrary convergence behavior is possible for the Arnoldi method and gives two parametrizations of the class of matrices with initial Arnoldi vectors that generates prescribed Ritz values. The second parametrization enables to prove that any GMRES convergence curve is possible with any prescribed Ritz values, provided the stagnation case is treated appropriately.

In the computer science curriculum, programming language holds a central importance as it enables the programmers to develop software more effectively. Every year, multiple programming languages are proposed, designed and implemented to keep up with the changing programming paradigms, hardware evolution, etc. The current article presents a comparative study of three programming languages C, Java, and PHP. Different aspects of the languages were studied in order to know their structure. Additionally, t he results received from all three languages were implemented on a medical theory to analyze the performance.

As vocabulary is an important component of language teaching and there exist certain problems in students’ vocabulary skills, traditional and modern teaching methods used in Turkish as a foreign language teaching are discussed in the article. The frequency of use and the success rates were taken into consideration in the determination of the methods. In this context, a survey was developed and administered within Analytic Hierarchy Process (AHP) for teachers of Turkish to foreigners in order to determine the significance level of vocabulary teaching methods in Turkish as a foreign language. The survey consisted of comparative questions for determining the significance levels of vocabulary acquisition methods used in teaching Turkish as a foreign language. The data collected in this research were analyzed in Microsoft Excel program and the results were presented as statistical tables. According to the findings, the significance level of communicative teaching methods conducted throug...

Land Use and Land Cover (LULC) maps derived from satellite images are a significant source of geo-information to better understand the current status of landscapes, to analyze the landscape changes, and to develop sustainable decisions for landscape and urban planning. Since the spectral and spatial resolution of satellite images directly impact the LULC classes to be identified and the accuracy of the classification, these will also affect the values of calculated landscape metrics. This research aims to propose the most appropriate functions and features to obtain highly accurate thematically extensive LULC classification results from multi-resolution satellite images and to investigate how the change in spatial resolution of satellite images would affect the landscape metrics values and landscape pattern analysis Sentinel-2, SPOT-7, Pleaides, and Worldview-4 images with respective 10 m, 1.5 m, 0.5 m, and 0.3 m spatial resolution were classified using Geographic Object-Based Image...

Statistical literacy" is important to be an effective citizen . Towards "probability literacy" for all citizens: Building blocks and instructional dilemmas. In: G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). New York: Springer]). Probability and statistics has been connected with real context and can be used to stimulate students' creative abilities. This study aims at identifying the extent that textbooks in three countries include experimental probability concepts and non-routine, open-ended, application and contextual problems. How well textbooks reflect real application situations is important in the sense that students can employ probability concepts when solving real world problems. Results showed that three textbook series did not mention experimental probability. Furthermore, all of textbooks had more routine, close-ended, knowing, and non-contextual problems.

Life Cycle Assessment (LCA) studies the environmental impact of products taking into account their entire life-span and production chain. This requires gathering data from a variety of heterogeneous sources into a Life Cycle Inventory (LCI). LCI preparation involves the integration of observations and engineering models with reference data and literature results from around the world, from different domains, and at varying levels of granularity. Existing LCA data formats only address syntactic interoperability, thereby ignoring semantics. This leads to a variety of challenges, e.g., difficulties in reproducing assessments published in the literature. In this work, we present an ontology pattern that specifies key aspects of LCA/LCI data models, namely the notions of flows, activities, agents, and products, as well as their properties.

En raison de la capacite et de l'amelioration des performances informatiques, les representations structurelles sont devenues de plus en plus populaires dans le domaine de la reconnaissance de formes (RF). Quand les objets sont structures a base de graphes, le problme de la comparaison d'objets revient a un problme d'appariement de graphes (Graph Matching). Au cours de la derniere decennie, les chercheurs travaillant dans le domaine de l'appariement de graphes ont porte une attention particuliere a la distance d'edition entre graphes (GED), notamment pour sa capacite a traiter different types de graphes. GED a ete ainsi appliquee sur des problematiques specifiques qui varient de la reconnaissance de molecules a la classi fication d'images.

Graph Distance Contest (GDC) was organized in the context of ICPR 2016. Its main challenge was to inspect and report performances and effectiveness of exact and approximate graph edit distance methods by comparison with a ground truth. This paper presents the context of this competition, the metrics and datasets used for evaluation, and the results obtained by the eight submitted methods. Results are analyzed and discussed in terms of computation time and accuracy. We also highlight the future challenges in graph edit distance regarding both future methods and evaluation metrics. The contest was supported by the Technical Committee on Graph-Based Representations in Pattern Recognition (TC-15) of the International Association of Pattern Recognition (IAPR).

This paper presents a binary linear program which computes the exact graph edit distance between two richly attributed graphs (i.e. with attributes on both vertices and edges). Without solving graph edit distance for large graphs, the proposed program enables to process richer and larger graphs than existing approaches based on mathematical programming and the A * algorithm. Experiments are led on 7 standard graph datasets and the proposed approach is compared with two stateof-the-art algorithms.

Forum is a huge space where people from different geographical location can express and share their own opinions, influencing any aspect of life by marketing and communication. On one side, Monitoring suspicious communication on these forums is the best way to measure the loyalty of users. On the other side, Many malicious people use these discussion forums for illegal purpose by posting suspicious chats in the form of text, video or images, exchange them with other users. The law enforcement agencies are looking for solutions to monitor these communication forums for possible criminal activities. Mostly the data stored in chat forums are in the form of text, so the proposed system will focus only on text posts. Considering this scenario, I propose a system which tackle this problem. Monitoring the malicious activities is the best way to calculate the user’s honesty, keeping a track of their sentiment toward their chats. The exponential advancement in information and communication t...

The current paper exposes the development of a game application that combines augmented reality, modern robotics, mobile features and multiplayer networking in order to create an immersive collaboration system, where people can interconnect to have fun and complete entertaining tasks together. SMAUG is a game based on Sphero 2.0 robotic ball, where multiple players share the same driving control of the robot. Depending on the game session and quest, a player can influence a certain moving direction or the robot's speed. Furthermore, the playground is augmented on the driving surface, so each player is looking to the game scene through his/her mobile’s camera. The main objective here is that players need to collaborate in order to accomplish various tasks: collecting game artifacts, drive on augmented tracks, break down walls/gates, escape mazes and so on. In order to accomplish this objective the game is demanding collaboration: the game artifacts are distributed to different pl...

We model the edit distance as a function in a labelling space. A labelling space is an Euclidean space where coordinates are the edit costs. Through this model, we define a class of cost. A class of cost is a region in the labelling space that all the edit costs have the same optimal labelling. Moreover, we characterise the distance value through the labelling space. This new point of view of the edit distance gives as the opportunity of defining some interesting properties that are useful for a better understanding of the edit distance. Finally, we show the usefulness of these properties through some applications.

Bipartite (BP) has been seen to be a fast and accurate suboptimal algorithm to solve the Error-Tolerant Graph Matching problem. Recently, Fast Bipartite (FBP) has been presented that obtains the same distance value and node labelings but in a reduced time. Both algorithms approximate the quadratic problem in a linear problem and they do it through a specific cost matrix. FBP imposes the Edit costs to be defined such as the Edit distance is a distance function. Originally, the Hungarian method was used but it has been seen the Jonker–Volgenant linear solver obtains similar results than the Hungarian method but with an important run time reduction. Nevertheless, this second solver has some convergence problems on some specific cost matrices. The aim of this paper is to define a new cost matrix such that the Jonker–Volgenant solver converges and the matching algorithm obtains the same distance value than the BP algorithm.

The graph edit distance (GED) is a flexible and widely used dissimilarity measure between graphs. Computing the GED between two graphs can be performed by solving a quadratic assignment problem (QAP). However, the problem is NP complete hence forbidding the computation of the optimal GED on large graphs. To tackle this drawback, recent heuristics are based on a linear approximation of the initial QAP formulation. In this paper, we propose a method providing a better local minimum of the QAP formulation than our previous proposition based on IPFP. We adapt a convex concave regularization scheme initially designed for graph matching which allows to reach better local minimum and avoids the need of an initialization step. Several experiments demonstrate that our method outperforms previous methods in terms of accuracy, with a time still much lower than the computation of a GED.

Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.  GED computation is proved to be NP-hard, which could result in unsatisfactory computational efficiency on large graphs. However, exactly accurate search results are usually unnecessary for real-world applications .Thus, in this paper, we propose a novel probabilistic approach to efficiently estimate GED, which is further leveraged for the graph similarity search. Specifically, we first take branches as elementary structures in graphs, and  a novel graph similarity measure by comparing branches between graphs, i.e., Graph Branch Distance (GBD).Then, we formulate the relationship between GED and GBD by considering branch variations .The GED between any two graphs can be efficiently estimated by their GBD, and these estimations are finally utilized in the graph similarity search. experiments show that our approach has better accuracy, efficiency and scalability than other comparable methods

A device for queue management Which can receive and trans mit a Short Message Service (SMS) text. The patient or cus tomer Would be the sender requesting a queue number via SMS. Phone caller ID Will also be utiliZed. Thereafter the queue management device or computer system Will generate a queue number and send back to the patient or customer via SMS the requested queue number, the estimated time of ser vice and/or approximate time that customer must be present at the Waiting hall as Well as current number of customer being served. Also a LED display and computing device Will display current queue number being served as Well. The Walk in customer can also press the touch screen button to get the printed queue ticket. The printed queue number Will be con sistent and concurrent With queue numbers issued and sent to remote customers.

Bipartite (BP) has been seen to be a fast and accurate suboptimal algorithm to solve the Error-Tolerant Graph Matching problem. Recently, Fast Bipartite (FBP) has been presented that obtains the same distance value and node labelings but in a reduced time. Both algorithms approximate the quadratic problem in a linear problem and they do it through a speci¯c cost matrix. FBP imposes the Edit costs to be de¯ned such as the Edit distance is a distance function. Originally, the Hungarian method was used but it has been seen the Jonker-Volgenant linear solver obtains similar results than the Hungarian method but with an important run time reduction. Nevertheless, this second solver has some convergence problems on some speci¯c cost matrices. The aim of this paper is to de¯ne a new cost matrix such that the Jonker-Volgenant solver converges and the matching algorithm obtains the same distance value than the BP algorithm.