Redundant Vertices Research Articles

Efficient Path Planning Algorithm Based on Laser SLAM and an Optimized Visibility Graph for Robots

Mobile robots’ efficient path planning has long been a challenging task due to the complexity and dynamism of environments. If an occupancy grid map is used in path planning, the number of grids is determined by grid resolution and the size of the actual environment. Excessively high resolution increases the number of traversed grid nodes and thus prolongs path planning time. To address this challenge, this paper proposes an efficient path planning algorithm based on laser SLAM and an optimized visibility graph for mobile robots, which achieves faster computation of the shortest path using the optimized visibility graph. Firstly, the laser SLAM algorithm is used to acquire the undistorted LiDAR point cloud data, which are converted into a visibility graph. Secondly, a bidirectional A* path search algorithm is combined with the Minimal Construct algorithm, enabling the robot to only compute heuristic paths to the target node during path planning in order to reduce search time. Thirdly, a filtering method based on edge length and the number of vertices of obstacles is proposed to reduce redundant vertices and edges in the visibility graph. Additionally, the bidirectional A* search method is implemented for pathfinding in the efficient path planning algorithm proposed in this paper to reduce unnecessary space searches. Finally, simulation and field tests are conducted to validate the algorithm and compare its performance with classic algorithms. The test results indicate that the method proposed in this paper exhibits superior performance in terms of path search time, navigation time, and distance compared to D* Lite, FAR, and FPS algorithms.

Branch-Price-and-Cut algorithms for the team orienteering problem with interval-varying profits

This paper studies the team orienteering problem (TOP), wherein each vertex requires two visits, and the service profit of each vertex depends on the time interval between these two visits. Motivated by scenarios like perishable product delivery, home health care scheduling, and earth observation satellite scheduling, the paper addresses two variants: the periodic orienteering problem with a focus on the number of days (NoDs) and the team orienteering problem with attention to a combination of time windows (CoTWs). It develops mixed-integer linear programming (MILP) models for both variants and devises exact Branch-Price-and-Cut (BPC) algorithms tailored to their block diagonal structures. Furthermore, this paper proposes two strategies to improve algorithm performance. A simplification strategy streamlines the directed graph network by removing redundant vertices and arcs without compromising optimality, thereby accelerating the solution of pricing problems. Additionally, a matheuristic algorithm is proposed to obtain integer solutions quickly. Computational results demonstrate the effectiveness of these algorithms, showcasing their superiority over CPLEX. The BPC algorithm, coupled with the simplification strategy, exhibits an average computational time reduction of 70 % compared to the basic strategy. The effectiveness of the matheuristic algorithm is also confirmed. Finally, the findings presented herein offer valuable insights for refining and applying BPC algorithms.

Efficient Distributed Hop-Constrained Path Enumeration on Large-Scale Graphs

The enumeration of hop-constrained simple paths is a building block in many graph-based areas. Due to the enormous search spaces in large-scale graphs, a single machine can hardly satisfy the requirements of both efficiency and memory, which causes an urgent need for efficient distributed methods. In practice, it is inevitable to produce plenty of intermediate results when directly extending centralized methods to the distributed environment, thereby causing a memory crisis and weakening the query performance. The state-of-the-art distributed method HybridEnum designed a hybrid search paradigm to enumerate simple paths. However, it makes massive exploration for the redundant vertices not located in any simple path, thereby resulting in poor query performance. To alleviate this problem, we design a distributed approach DistriEnum to optimize query performance and scalability with well-bound memory consumption. Firstly, DistriEnum adopts a graph reduction strategy to rule out the redundant vertices without satisfying the constraint of hop number. Then, a core search paradigm is designed to simultaneously reduce the traversal of shared subpaths and the storage of intermediate results. Moreover, DistriEnum is equipped with a task division strategy to theoretically achieve workload balance. Finally, a vertex migration strategy is devised to reduce the communication cost during the enumeration. The comprehensive experimental results on 10 real-world graphs demonstrate that DistriEnum achieves up to 3 orders of magnitude speedup than HybridEnum in query performance and exhibits superior performances on scalability, communication cost, and memory consumption.

Move and remove: Multi-task learning for building simplification in vector maps with a graph convolutional neural network

Simplification of building footprints is an essential task in topographic map generalization from large to medium scales. The traditional rule- or constraint-based algorithms commonly require cartographers to enumerate and formalize as many scenarios as possible. Recently, some studies have introduced deep learning to image map generalization, whose outputs, however, may exhibit deformed boundaries due to pure image input. Vector maps are thus a reasonable solution to avoid such issues because of their accurate, object-based geometric representation. However, few existing studies have aimed to simplify buildings in vector maps with the help of neural networks. Building simplification in vector maps can be regarded as the joint contribution from two elementary operations on vertices of building polygons: remove redundant vertices and move kept vertices. This research proposes a multi-task learning method with graph convolutional neural networks. The proposed method formulates the building simplification problem as a joint task of node removal classification and node movement regression. A multi-task graph convolutional neural network model (MT_GCNN) is developed to learn node removal and movement simultaneously. The model was evaluated with a map from Stuttgart, Germany that contains 8494 buildings generalized from the source scale of 1:5,000 to the target scale of 1:10,000. The experimental results show that the proposed method can generate 80% of the buildings with positional errors of less than 0.2 m, 95% with a shape difference under 0.5, and around 98% with an area difference under 0.1 of IoU, compared to the ground truth target buildings, thus demonstrating the feasibility of the proposed method. The code is available at: https://github.com/chouisgiser/MapGeneralizer.

PolyBuilding: Polygon transformer for building extraction

We present PolyBuilding, a polygon Transformer for building extraction. PolyBuilding direct predicts vector representation of buildings from remote sensing images. It builds upon an encoder–decoder transformer architecture and simultaneously predicts the bounding boxes and polygons for the building instances. Given a set of polygon queries, the model learns the relations among them and encodes context information from the image to predict the final set of building polygons with a fixed vertex number. Considering that predicting a fixed number of vertices would cause vertex redundancy and reduce polygon regularity, we design a corner classification head to distinguish the building corners. By taking advantage of the corner classification scores, a polygon refinement scheme is designed to remove the redundant vertices and produce the final polygons with regular contours and low complexity. In addition, although the PolyBuilding model is fully end-to-end trainable, we propose a two-phase training strategy to decompose the coordinate regression and corner classification into two stages to alleviate the difficulty of multi-task learning. Comprehensive experiments are conducted on the CrowdAI dataset and Inria dataset. PolyBuilding achieves a new state-of-the-art in terms of pixel-level coverage, instance-level detection performance, and geometry-level properties. Quantitative and qualitative results verify the superiority and effectiveness of our model.

An Exact Algorithm with New Upper Bounds for the Maximum k-Defective Clique Problem in Massive Sparse Graphs

The Maximum k-Defective Clique Problem (MDCP), as a clique relaxation model, has been used to solve various problems. Because it is a hard computational task, previous works can hardly solve the MDCP for massive sparse graphs derived from real-world applications. In this work, we propose a novel branch-and-bound algorithm to solve the MDCP based on several new techniques. First, we propose two new upper bounds of the MDCP as well as corresponding reduction rules to remove redundant vertices and edges. The proposed reduction rules are particularly useful for massive graphs. Second, we present another new upper bound by counting missing edges between fixed vertices and an unfixed vertex for cutting branches. We perform extensive computational experiments to evaluate our algorithm. Experimental results show that our reduction rules are very effective for removing redundant vertices and edges so that graphs are reduced greatly. Also, our algorithm can solve benchmark instances efficiently, and it has significantly better performance than state-of-the-art algorithms.

Graph Sampling Through Graph Decomposition and Reconstruction Based on Kronecker Graphs

The connectedness of the social network gives rise to a new challenge of how to efficiently sample the network and keep the graph properties and topology properties as well. Inspired by R-MAT and Kronecker graph generators, based on the observation of different graph topology types, we proposed to use Kronecker graph as the prime graph to conduct Kronecker graph double cover through periphery subgraphs. First of all, the connectedness of the graph remains during graph merging. Secondly, only redundant vertices and edges are merged so that the characteristics of the graphs are kept. Also, graph merging only works on periphery subgraphs from low degrees to higher up so those topology properties are kept. Finally, although some edges are merged, since the similarity groups generated based on Kronecker graph similarity is independent of the degree distribution, Kronecker double cover operation does not affect the graph degree centrality measure. We theoretically prove the feasibility of the Kronecker double-cover operation and also compare the quality of the sample set with Snowball sampling and Es-i sampling sets. Experimental results show us that, when the separation of the core and periphery subgraphs is between mean (the average of the degrees) and mean+std (standard deviation of the degrees), the topology types and graph properties can be preserved. This conclusion confirms the existence of the topology types, and also proves the topology types of the real-world graphs are not random.

A Concentric Loop Convolutional Neural Network for Manual Delineation-Level Building Boundary Segmentation From Remote-Sensing Images

To date, accurate building footprint delineation in the surveying, mapping, and geographic information system (GIS) communities has been dependent on human labor. In this article, to address this issue, we propose a concentric loop convolutional neural network (CLP-CNN) method for the automatic segmentation of building boundaries from remote-sensing images. The proposed method consists of three components: 1) a boundary detector to extract coarse polygonal boundaries of individual regions of interest; 2) a concentric loop-shaped convolutional network with bidirectional pairing loss to fine-tune the vertices of the polygons; and 3) a refinement block, which removes redundant vertices and regularizes the boundaries to polygons at the manual delineation level. We also demonstrate that the proposed CLP-CNN method is applicable to other generic objects in natural images. Experiments on two building datasets confirmed that more than 77%/67% of the building polygons predicted by the proposed method are on par with the manual delineation level, representing a significant saving in the labor cost of manual annotation. In generic object boundary delineation tests performed on the Semantic Boundaries Dataset (SBD), the proposed method outperformed the most recent state-of-the-art methods by at least 3.1% in average precision (AP). Furthermore, compared with other vertex matching methods, the learning process of the proposed method converges faster. The source code will be available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">http://gpcv.whu.edu.cn/data</uri> .

A restart local search algorithm with Tabu method for the minimum weighted connected dominating set problem

The minimum weighted connected dominating set problem is a significant NP-hard problem with wide applications, and is an extension of the classical minimum dominating set problem. In order to solve this problem, we present a restart local search algorithm with tabu method (RLS Tabu). In our RLS Tabu algorithm, we firstly involve the random restart initialization method to jump out of the local optimum. Meanwhile, RLS Tabu algorithm also applies tabu method in neighborhood search procedure to mitigate the cycling problem. Secondly, we present two strategies in neighborhood search procedure for removing vertices properly, which one is greedy and random strategy, and another one is multiple deletion strategy. The two strategies are crucial to improve the solution quality. Thirdly, the solution connected vertex is important to guarantee the feasibility of solutions. Therefore, we maintain the solution connected vertex set during the neighborhood search, and select the vertex to be added from this set. Finally, in order to intensify the solution, RLS Tabu utilizes the pruning function to delete redundant vertices in the candidate solution. In experimental section, we will compare our algorithm with the other six algorithms on three types of benchmarks. Experimental results indicate that our algorithm significantly outperforms the comparative algorithms on most benchmark instances.

Improving Maximum k-plex Solver via Second-Order Reduction and Graph Color Bounding

In a graph, a k-plex is a vertex set in which every vertex is not adjacent to at most k vertices of this set. The maximum k-plex problem, which asks for the largest k-plex from the given graph, is a key primitive in a variety of real-world applications like community detection and so on. In the paper, we develop an exact algorithm, Maplex, for solving this problem in real world graphs practically. Based on the existing first-order and the novel second-order reduction rules, we design a powerful preprocessing method which efficiently removes redundant vertices and edges for Maplex. Also, the graph color heuristic is widely used for overestimating the maximum clique of a graph. For the first time, we generalize this technique for bounding the size of maximum k-plex in Maplex. Experiments are carried out to compare our algorithm with other state-of-the-art solvers on a wide range of publicly available graphs. Maplex outperforms all other algorithms on large real world graphs and is competitive with existing solvers on artificial dense graphs. Finally, we shed light on the effectiveness of each key component of Maplex.

On new algorithmic techniques for the weighted vertex coloring problem

The classical NP-hard weighted vertex coloring problem consists in minimizing the number of colors in colorings of vertices of a given graph so that, for each vertex, the number of its colors equals a given weight of the vertex and adjacent vertices receive distinct colors. The weighted chromatic number is the smallest number of colors in these colorings. There are several polynomial-time algorithmic techniques for designing efficient algorithms for the weighted vertex coloring problem. For example, standard techniques of this kind are the modular graph decomposition and the graph decomposition by separating cliques. This article proposes new polynomial-time methods for graph reduction in the form of removing redundant vertices and recomputing weights of the remaining vertices so that the weighted chromatic number changes in a controlled manner. We also present a method of reducing the weighted vertex coloring problem to its unweighted version and its application. This paper contributes to the algorithmic graph theory.

Operational-space wrench and acceleration capability analysis for multi-link cable-driven robots

Multi-link cable-driven robots (MCDRs) have potential advantages in confined spaces exploration because of their redundancy and flexibility. Operational space wrench and acceleration capability analysis of MCDRs is important for their design, manipulability optimization, and motion planning. However, existing works mainly focus on capability analysis in the joint space. In this paper, we present a zonotope-based iterative method and a simplified capability zonotope to analyze the operational-space wrench and acceleration capability of MCDRs. In the iterative method, the capability generated by some cables can be iteratively added to the initial capability zonotope based on the Minkowski sum. In the simplified zonotope capability representation, a threshold is put forward to reduce redundant vertices and faces with little volume loss. Finally, simulations on a 24 DOFs MCDR are performed to verify the effectiveness of the developed method. The results demonstrate that our iterative algorithm can easily generate the capability zonotope with a few MB ROM, while traditional operational wrench capability evaluation without our iterative algorithm needs 18432 GB ROM. Furthermore, our simplified representation reduces the vertices and faces from 1260 and 2516 to 88 and 172, respectively, but with only 3.3% volume loss, which decreases the constraints of the robot and is conducive to manipulability optimization and motion planning.

Network topology inference using information cascades with limited statistical knowledge

AbstractWe study the problem of inferring network topology from information cascades, in which the amount of time taken for information to diffuse across an edge in the network follows an unknown distribution. Unlike previous studies, which assume knowledge of these distributions, we only require that diffusion along different edges in the network be independent together with limited moment information (e.g. the means). We introduce the concept of a separating vertex set for a graph, which is a set of vertices in which for any two given distinct vertices of the graph there exists a vertex whose distance to them is different. We show that a necessary condition for reconstructing a tree perfectly using distance information between pairs of vertices is given by the size of an observed separating vertex set. We then propose an algorithm to recover the tree structure using infection times whose differences have means corresponding to the distance between two vertices. To improve the accuracy of our algorithm, we propose the concept of redundant vertices, which allows us to perform averaging to better estimate the distance between two vertices. Though the theory is developed mainly for tree networks, we demonstrate how the algorithm can be extended heuristically to general graphs. Simulations using synthetic and real networks and experiments using real-world data suggest that our proposed algorithm performs better than some current state-of-the-art network reconstruction methods.

An efficient simplification method for point cloud based on salient regions detection

Many computer vision approaches for point clouds processing consider 3D simplification as an important preprocessing phase. On the other hand, the big amount of point cloud data that describe a 3D object require excessively a large storage and long processing time. In this paper, we present an efficient simplification method for 3D point clouds using weighted graphs representation that optimizes the point clouds and maintain the characteristics of the initial data. This method detects the features regions that describe the geometry of the surface. These features regions are detected using the saliency degree of vertices. Then, we define features points in each feature region and remove redundant vertices. Finally, we will show the robustness of our methodviadifferent experimental results. Moreover, we will study the stability of our method according to noise.

Analysis of Critical and Redundant Vertices in Controlling Directed Complex Networks Using Feedback Vertex Sets.

Controlling complex networks through a small number of controller vertices is of great importance in wide-ranging research fields. Recently, a new approach based on the minimum feedback vertex set (MFVS) has been proposed to find such vertices in directed networks in which the target states are restricted to steady states. However, multiple MFVS configurations may exist and thus the selection of vertices may depend on algorithms and input data representations. Our attempts to address this ambiguity led us to adopt an existing approach that classifies vertices into three categories. This approach has been successfully applied to maximum matching-based and minimum dominating set-based controllability analysis frameworks. In this article, we present an algorithm as well as its implementation to compute and evaluate the critical, intermittent, and redundant vertices under the MFVS-based framework, where these three categories include vertices belonging to all MFVSs, some (but not all) MFVSs, and none of the MFVSs, respectively. The results of computational experiments using artificially generated networks and real-world biological networks suggest that the proposed algorithm is useful for identifying these three kinds of vertices for relatively large-scale networks, and that the fraction of critical and intermittent vertices is considerably small. Moreover, an analysis of the signal pathways indicates that critical and intermittent MFVSs tend to be enriched by essential genes.

Molecular Surface Remeshing with Local Region Refinement.

Molecular surface mesh generation is a prerequisite for using the boundary element method (BEM) and finite element method (FEM) in implicit-solvent modeling. Molecular surface meshes typically have small angles, redundant vertices, and low-quality elements. In the implicit-solvent modeling of biomolecular systems it is usually required to improve the mesh quality and eliminate low-quality elements. Existing methods often fail to efficiently remove low-quality elements, especially in complex molecular meshes. In this paper, we propose a mesh refinement method that smooths the meshes, eliminates invalid regions in a cut-and-fill strategy, and improves the minimal angle. We compared our method with four different state-of-the-art methods and found that our method showed a significant improvement over state-of-the-art methods in minimal angle, aspect ratio, and other meshing quality measurements. In addition, our method showed satisfactory results in terms of the ratio of regular vertices and the preservation of area and volume.

Explicit bounds for graph minors

Let Σ be a surface with boundary bd(Σ), L be a collection of k disjoint bd(Σ)-paths in Σ, and P be a non-separating bd(Σ)-path in Σ. We prove that there is a homeomorphism ϕ:Σ→Σ that fixes each point of bd(Σ) and such that ϕ(L) meets P at most 2k times.With this theorem, we derive explicit constants in the graph minor algorithms of Robertson and Seymour (1995) [10]. We reprove a result concerning redundant vertices for graphs on surfaces, but with explicit bounds. That is, we prove that there exists a computable integer t:=t(Σ,k) such that if v is a ‘t-protected’ vertex in a surface Σ, then v is redundant with respect to any k-linkage.

An analytical method on the stabilization of fractional-order plants with one fractional-order term and interval uncertainties using fractional-order PIλ Dμ controllers

In this study, we propose an analytical method to determine the stabilization of fractional-order plants with one fractional-order term and interval uncertainties using fractional-order [Formula: see text][Formula: see text] controllers. An auxiliary function related to the characteristic function of the closed-loop system is defined, and the real vertices and edges of the value set with respect to the auxiliary function are given by the Minkowski sum method. It can effectively reduce the computation burden caused by redundant vertices. The concept of switching frequencies is proposed, and the calculation method of switching frequencies is provided. In order to test the position relationship between the value set and the origin within a finite frequency interval, the upper and lower limits of the frequency interval are calculated and the mathematical expressions of the vertices in each frequency interval determined by the switching frequencies and limits are given. Based on the analysis of the position relationship, we propose the necessary and sufficient condition of the stabilization criterion. Finally, the stabilization problems of the numerical examples are analysed to verify the effectiveness of the proposed stabilization criterion.

Robust stabilization of interval fractional-order plants with one time-delay by fractional-order controllers

This study investigates the robust stabilization of interval fractional-order plants with one time-delay using fractional-order controllers by the Minkowski sum of value sets. The characteristic function of a closed loop system in terms of the fractional-order controller and an interval fractional-order plant with one time-delay is divided into the nominal function and disturbance function. By the Minkowski sum, the value set of disturbance function is obtained to avoid the calculation for the redundant vertices. Based on the zero exclusion principle, the robust stabilization conditions are provided. The computing method of the upper and lower limits of a finite frequency interval is offered to achieve the test operation of the robust stabilization criterion. Under the assumption that the fractional-order controller can stabilize the nominal plant, three conditions in the proposed theorem ensure that the corresponding fractional-order controller can stabilize the interval fractional-order plant with one time-delay. Finally, two illustrative examples are provided to verify the effectiveness of this proposed robust stabilization criterion.

Robust stabilization criterion of fractional-order controllers for interval fractional-order plants

The robust stabilization criterion of fractional-order controllers for interval fractional-order plants is proposed in this study. For the interval uncertainties existing in the numerator and denominator of a transfer function with respect to a fractional-order plant, the vertices of the value set corresponding to the characteristic function are offered by the Minkowski Sum. This algorithm for getting the vertices avoids to calculate the redundant vertices, reducing the computational complexity. An auxiliary function reflecting the position relationship between the origin and the value set is defined to investigate the robust stability conditions. The lower and upper limits of the test frequency interval are offered to check the auxiliary function within a finite frequency. Supposing that the fractional-order controller can stabilize the nominal fractional-order plant, the stabilization criterion of the closed loop system with interval uncertainties is provided based on the auxiliary function and other two conditions. Finally, three illustrative examples with fractional-order controllers are given to validate the effectiveness of this robust stabilization criterion.