B-splines in EMD and Graph Theory in Pattern Recognition

With the development of science and technology, a large amount of data is waiting for further scientific exploration. We can always build up some good mathematical models based on the given data to analyze and solve the real life problems. In this work, we propose three types of mathematical models for different applications.;In chapter 1, we use Bspline based EMD to analysis nonlinear and no-stationary signal data. A new idea about the boundary extension is introduced and applied to the Empirical Mode Decomposition(EMD) algorithm. Instead of the traditional mirror extension on the boundary, we propose a ratio extension on the boundary.;In chapter 2 we propose a weighted directed multigraph for text pattern recognition. We set up a weighted directed multigraph model using the distances between the keywords as the weights of arcs. We then developed a keyword-frequency-distance-based algorithm which not only utilizes the frequency information of keywords but also their ordering information.;In chapter 3, we propose a centrality guided clustering method. Different from traditional methods which choose a center of a cluster randomly, we start clustering from a LEADER - a vertex with highest centrality score, and a new member is added into an existing community if the new vertex meet some criteria and the new community with the new vertex maintain a certain density.;In chapter 4, we define a new graph optimization problem which is called postman tour with minimum route-pair cost. And we model the DNA sequence assembly problem as the postman tour with minimum route-pair cost problem

Eulerian Paths with Regular Constraints

Labeled graphs, in which edges are labeled by letters from some alphabet Sigma, are extensively used to model many types of relations associated with actions, costs, owners, or other properties. Each path in a labeled graph induces a word in Sigma^* -- the one obtained by concatenating the letters along the edges in the path. Classical graph-theory problems give rise to new problems that take these words into account. We introduce and study the constrained Eulerian path problem. The input to the problem is a Sigma-labeled graph G and a specification L subseteq Sigma^*. The goal is to find an Eulerian path in G that satisfies L. We consider several classes of the problem, defined by the classes of G and L. We focus on the case L is regular and show that while the problem is in general NP-complete, even for very simple graphs and specifications, there are classes that can be solved efficiently. Our results extend work on Eulerian paths with edge-order constraints. We also study the constrained Chinese postman problem, where edges have costs and the goal is to find a cheapest path that contains each edge at least once and satisfies the specification. Finally, we define and study the Eulerian language of a graph, namely the set of words along its Eulerian paths

The target visitation arc routing problem

This paper studies the target visitation arc routing problem on an undirected graph. This problem combines the well-known undirected rural postman problem and the linear ordering problem. In this problem, there is a set of required edges partitioned into targets, which must be traversed and there are pairwise preferences for the order in which some targets are serviced, which generates a revenue if the preference is satisfied. The aim is to find a tour that traverses all required edges at least once, and offers a compromise between the revenue generated by the order in which targets are serviced, and the routing cost of the tour. A linear integer programming formulation including some families of valid inequalities is proposed. Despite the difficulty of the problem, the model can be used to solve to optimality around 62% of the test instances.</p

The target visitation arc routing problem

This paper studies the target visitation arc routing problem on an undirected graph. This problem combines the well-known undirected rural postman problem and the linear ordering problem. In this problem, there is a set of required edges partitioned into targets, which must be traversed and there are pairwise preferences for the order in which some targets are serviced, which generates a revenue if the preference is satisfied. The aim is to find a tour that traverses all required edges at least once, and offers a compromise between the revenue generated by the order in which targets are serviced, and the routing cost of the tour. A linear integer programming formulation including some families of valid inequalities is proposed. Despite the difficulty of the problem, the model can be used to solve to optimality around 62% of the test instances.</p

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

Multi-robot Boundary Coverage with Plan Revision

This paper revisits the multi-robot boundary coverage problem in which a group of k robots must inspect every point on the boundary of a 2-dimensional environment. We focus on the case in which revision of the original inspection plan may be necessary due to changes in the robot team size or the environment. Building upon prior work, which presented a graph-based approach to path planning for this problem, we present a graph representation of the task that is greatly reduced in complexity and a path revision algorithm appropriate for addressing such changes

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

A Constraint-Solving Approach for Achieving Minimal-Reset Transition Coverage of Smartcard Behaviour

Smartcards are security critical devices requiring a high assurance verification approach. Although formal techniques can be used at design or even at development stages, such systems have to undergo a traditional hardware-in-the-loop testing phase. This phase is subject to two key requirements: achieving exhaustive transition coverage of the behavior of the system under test, and minimizing the testing time. In this context, testing time is highly bound to a specific hardware reset operation. Model-based testing is the adequate approach given the availability of a precise model of the system behavior and its ability to produce high quality coverage while optimizing some cost criterion. %l'argument n'est pas convainquant.This paper presents an original algorithm addressing this problem by reformulating it as an integer programming problem to make a graph Eulerian. The associated cost criterion captures both the number of resets and the total length of the test suite, as an auxiliary objective. The algorithm ensures transition coverage. An implementation of the algorithm was developed, benchmarked, and integrated into an industrial smartcard testing framework. A validation case study from this domain is also presented. The approach can of course be applied to any other domains with similar reset-related testing constraints