Coverage Problem Research Articles

On the secure vertex cover pebbling number

A new graph invariant called the secure vertex cover pebbling number, which is a combination of two graph invariants, namely, ‘secure vertex cover’ and ‘cover pebbling number’, is introduced in this paper. The secure vertex cover pebbling number of a graph, [Formula: see text], is the minimum number [Formula: see text] so that every distribution of [Formula: see text] pebbles can reach some secure vertex cover of [Formula: see text] by a sequence of pebbling moves. In this paper, the complexity of the secure vertex cover problem and secure vertex cover pebbling problem are discussed. Also, we obtain some basic results and the secure vertex cover pebbling number for complete [Formula: see text]-partite graphs, paths, Friendship graphs, and wheel graphs.

EASC: An exception-aware semantic compression framework for real-world knowledge graphs

Knowledge graphs (KGs) have achieved great success in many real applications, and great efforts have been dedicated to constructing larger knowledge graphs. An obvious trend in KG construction is that the KGs become ever-increasingly bigger. However, we argue that constructing a KG by directly inserting more triples may harm the performance of the KG, and one possible solution is KG compression. In this paper, we propose an exception-aware semantic lossless compression framework EASC to compress a KG. Since many triples can be inferred from other triples with semantic rules, we remove the triples that can be inferred and store the rules and exception cases. Specifically, we formalize the lossless compression problem as a weighted set cover problem, which is NP-hard, and propose a semantic lossless compression algorithm to get an approximation result. We conduct extensive experiments on seven real-world large-scale KGs. The results show that EASC achieves state-of-the-art performance in semantic compression methods. Furthermore, by combining EASC as an independent module with syntactic compression methods, we achieve state-of-the-art performance in lossless compression methods.

Application of an Enhanced Whale Optimization Algorithm on Coverage Optimization of Sensor.

The wireless sensor network (WSN) is an essential technology of the Internet of Things (IoT) but has the problem of low coverage due to the uneven distribution of sensor nodes. This paper proposes a novel enhanced whale optimization algorithm (WOA), incorporating Lévy flight and a genetic algorithm optimization mechanism (WOA-LFGA). The Lévy flight technique bolsters the global search ability and convergence speed of the WOA, while the genetic optimization mechanism enhances its local search and random search capabilities. WOA-LFGA is tested with 29 mathematical optimization problems and a WSN coverage optimization model. Simulation results demonstrate that the improved algorithm is highly competitive compared with mainstream algorithms. Moreover, the practicality and the effectiveness of the improved algorithm in optimizing wireless sensor network coverage are confirmed.

Retracted: Mathematical Modeling and Simulation of Wireless Sensor Network Coverage Problem

Retracted: Mathematical Modeling and Simulation of Wireless Sensor Network Coverage Problem

A site selection framework for urban power substation at micro‐scale using spatial optimization strategy and geospatial big data

AbstractThe world is facing more energy crises due to extreme weather and the rapidly growing demand for electricity. Siting new substations and optimizing the location of existing ones are necessary to address the energy crisis. The current site selection lacks consideration of spatial and temporal heterogeneity in urban power demand, which results in unreasonable energy transfer and waste, leading to power outages in some areas. Aiming to maximize the grid coverage and transformer utilization, we propose a multi‐scene micro‐scale urban substation siting framework (UrbanPS): (1) The framework uses multi‐source big data and the machine learning model to estimate fine‐scale power consumption for different scenarios; (2) the region growing algorithm is used to divide the power supply area of substations; and the (3) location set coverage problem and genetic algorithm are introduced to optimize the substation location. The UrbanPS was used to perform siting optimization of 110 kV terminal substations in Pingxiang City, Jiangxi Province. Results show that the coverage and utilization rate of the optimization results under different power consumption scenarios are close to 99%. We also found that the power can be saved by dynamic regulation of substation operation.

A Multiple Mechanism Enhanced Arithmetic Optimization Algorithm for Numerical Problems.

The Arithmetic Optimization Algorithm (AOA) is a meta-heuristic algorithm inspired by mathematical operators, which may stagnate in the face of complex optimization issues. Therefore, the convergence and accuracy are reduced. In this paper, an AOA variant called ASFAOA is proposed by integrating a double-opposite learning mechanism, an adaptive spiral search strategy, an offset distribution estimation strategy, and a modified cosine acceleration function formula into the original AOA, aiming to improve the local exploitation and global exploration capability of the original AOA. In the proposed ASFAOA, a dual-opposite learning strategy is utilized to enhance population diversity by searching the problem space a lot better. The spiral search strategy of the tuna swarm optimization is introduced into the addition and subtraction strategy of AOA to enhance the AOA's ability to jump out of the local optimum. An offset distribution estimation strategy is employed to effectively utilize the dominant population information for guiding the correct individual evolution. In addition, an adaptive cosine acceleration function is proposed to perform a better balance between the exploitation and exploration capabilities of the AOA. To demonstrate the superiority of the proposed ASFAOA, two experiments are conducted using existing state-of-the-art algorithms. First, The CEC 2017 benchmark function was applied with the aim of evaluating the performance of ASFAOA on the test function through mean analysis, convergence analysis, stability analysis, Wilcoxon signed rank test, and Friedman's test. The proposed ASFAOA is then utilized to solve the wireless sensor coverage problem and its performance is illustrated by two sets of coverage problems with different dimensions. The results and discussion show that ASFAOA outperforms the original AOA and other comparison algorithms. Therefore, ASFAOA is considered as a useful technique for practical optimization problems.

Coverage Analysis for Elliptical-Orbit Satellites Based on 2-D Map

This paper proposes a geometric-based method of the ground-point visibility from a satellite or satellite constellation in elliptical orbit considering the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> perturbation. First, the field-element equations describing the relationship between the elliptical satellite orbit, field parameters, and ground point are introduced and can be solved semi-analytically. Also, using a two-dimensional map composed of the mean argument of latitude and geographic longitude of the ascending node, the problem of calculating visible intervals is transformed into a simple intersection problem of a group of parallel lines and a time-invariant region generated by the field-element equations. Furthermore, based on the geometric relationship between any two satellites, the relative field mapping and constellation field mapping are described, which can simplify the multi-satellite coverage problem to a single-satellite coverage problem and can be used to obtain the coverage performance of the constellation analytically and rapidly for the target. The simulation results demonstrate that the proposed method is rapid, efficient, intuitive, and accurate, suggesting its wide applications in constellation studies <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>

DQN-ALrM-Based Intelligent Handover Method for Satellite-Ground Integrated Network

The satellite-ground integrated network (SGIN), consisting of satellites and ground base stations, is regarded as the trend to solve the problem of global coverage. However, highly dynamic scenarios pose great challenges to users’ mobility management, especially handover decisions. With the rapid development of machine learning, reinforcement learning (RL), such as Q-learning and deep Q-network (DQN), has been applied to handover decision making owing to being good at solving dynamic multi-attribute optimization problems. However, Q-learning can be a waste of storage for large state spaces. Besides, the existing algorithms for training a neural network in a deep RL framework have problems of slow convergence or unstable convergence performance. Therefore, we propose a handover method exploiting the DQN framework of adaptive learning rate with momentum (DQN-ALrM), which can not only improve decision accuracy, but also improve learning efficiency. The customized DQN framework can solve problems with a large-size state space, and the proposed ALrM method can adjust the learning rate at any time according to the training error situation. Comprehensive simulations are conducted to validate the superiority of the proposed method in convergence speed, handover rate, call failure rate and multi-metric quality of service (QoS) over the alternative solutions in the literature.

Maximizing Energy Efficiency of Period-Area Coverage With a UAV for Wireless Rechargeable Sensor Networks

Wireless Rechargeable Sensor Networks (WRSNs) with perpetual network lifetime have been used in many Internet of Things (IoT) applications, like oceanic monitoring and precision agriculture. Rechargeable sensors, together with an Unmanned Aerial Vehicle (UAV), are collaboratively employed for fulfilling periodic coverage missions. However, traditional coverage solutions are normally based on static deployment of sensors and not suitable for such novel coverage requirements. In this paper, we propose the concept of Period-Area Coverage (PAC) problem, which requires the data of the overall area must be collected/monitored periodically. To solve the PAC problem, we employ a UAV that simultaneously acts as a mobile charger and sensor. It is responsible for charging nearly exhausted sensors and sensing vacant regions to realize complete event monitoring. To maximize the energy efficiency of the UAV, we propose a heuristic hexagon-based scheduling algorithm (HSA) which can also balance energy consumption. Furthermore, we develop an emergent node charging scheduling method to prevent node exhaustion, and introduce a grid-based boustrophedon scheduling algorithm (GBSA) to reduce the complexity. Finally, we present a charging re-allocation mechanism to further enhance energy efficiency. Extensive simulations demonstrate that the proposed schemes can solve the PAC problem and enhance energy efficiency by at least <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <inline-formula> <tex-math notation="LaTeX">$18.2\%$</tex-math> </inline-formula> </b> compared to prior arts. Test-bed experiments conducted both in agriculture and oceanic monitoring applications validate the applicability of the proposed scheme in practical scenarios.

Attacking the Core Structure of Complex Network

The concept of <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core in complex networks plays a key role in many applications, e.g., understanding the global structure or identifying central/critical nodes, of a network. A malicious attacker with a jamming ability can exploit the vulnerability of the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core structure to attack the network and invalidate the network analysis methods, e.g., reducing the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-shell values of nodes can deceive graph algorithms, leading to the wrong decisions. In this article, we investigate the robustness of the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core structure under adversarial attacks by deleting edges, for the first time. First, we give the general definition of the targeted <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core attack, map it to the set cover problem, which is NP-hard, and further introduce a series of evaluation metrics to measure the performance of attack methods. Then, we propose the <inline-formula> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> index theoretically as the probability that the terminal node of an edge does not belong to the innermost core, which is further used to guide the design of our heuristic attack methods, namely, COREATTACK and GreedyCOREATTACK. The experiments on a variety of real-world networks demonstrate that our methods behave much better than a series of baselines, in terms of much smaller edge change rate (ECR) and false attack rate (FAR), achieving state-of-the-art attack performance. More impressively, for certain real-world networks, only deleting one edge from the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core may lead to the collapse of the innermost core, even if this core contains dozens of nodes. Such a phenomenon indicates that the <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-core structure could be extremely vulnerable under adversarial attacks, and its robustness, thus, should be carefully addressed to ensure the security of many graph algorithms. An open-source implementation is available at https://github.com/Yocenly/COREATTACCK.

Vertex cover algorithm

Problem to solve P=NP, using the coverage problem of a graph that is NP and convert it to P. In the mathematical discipline of graph theory, a vertex cover, simply a graph cover, is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding the smallest vertex coverage in a graph is called the vertex coverage problem. In computational complexity theory, it has been shown that this is an NP-complete problem. An NPcomplete problem is that it is not known if it has a Polynomial solution. I have found an algorithm that proves that it is Polynomial.

The coverage and detection limit of a sampling point for robotics radiation mapping

The sensor coverage problem aims to maximize the coverage of a target area with a fixed or minimum number of sensors. However, the sampling point coverage for radiation mapping has yet to be specified or adequately established. When dealing with unknown radiation fields, it is critical that the placements of sampling points will ensure that all hotspots are detected and accurately identified. Therefore, the concept of coverage and detection limit for a sampling point in radiation mapping is proposed in this paper. The proposed concept relates the angular dependency of the radiation measurement instruments with the detector detection limit or minimum detectable amount (MDA). To demonstrate the implementation, the concept is used to compute the sensitivity of the radiation map for coverage radiation mapping with mobile robot. Simulation results showed that hotspots with intensity equal to or above the sampling point detection limit were successfully detected regardless of their position within the coverage circle. Moreover, the experimental results of coverage radiation mapping showed that the concept can be used to compute the resolution of the radiation map. This will help the user to efficiently configure the appropriate grid size that suit their mapping situation and requirements.

The single robot line coverage problem: Theory, algorithms, and experiments

AbstractLine coverage is the task of servicing a given set of one‐dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the required graph, that is, the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3 s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs on the UNC Charlotte campus road network.

An appraisal of Pharmacists’ involvement in Immunization delivery in Lagos State, Nigeria

Background The perennial problem of low immunization coverage in most developing countries calls for deployment of all available human health resources in order to increase access to life-saving vaccines and to increase immunization coverage. The aim of this study was to assess the knowledge, attitude and practice of pharmacists in immunization delivery and to explore barriers to involvement. Method: A pre- tested self-administered questionnaire was distributed to cross-section of 216 pharmacists working in secondary and tertiary hospitals across Lagos State, Nigeria. Knowledge and attitude scores were expressed as frequency and percentages. The Chi square test was used to explore association between demographic variables and respective scores. A p value of less than 0.05 was regarded as significant. Results: More than 80% of pharmacists were either very knowledgeable or fairly knowledgeable about vaccines and vaccine preventable diseases. Although there were concerns about regular power supply, resource availability was adequate but involvement in vaccine administration was low. Age and additional qualifications were significantly associated with knowledge of vaccines (X2 =18.594, df 4, P value=0.017, X2 =13.841, df 4, P value = 0.031 respectively). The major barriers to involvement were concerns about vaccine quality, availability and safety, lack of time, and lack of regular power supply. Conclusion Pharmacists’ knowledge on immunization was adequate but involvement in vaccine administration was low. The major barriers to involvement were concerns about vaccine quality, availability and safety. The option of deploying pharmacists for primary care duties, including immunization, appears plausible.

There is no APTAS for 2-dimensional vector bin packing: Revisited

We study the Vector Bin Packing and the Vector Bin Covering problems, multidimensional generalizations of the Bin Packing and the Bin Covering problems, respectively. In the Vector Bin Packing, we are given a set of d-dimensional vectors from [0,1]d and the aim is to partition the set into the minimum number of bins such that for each bin B, each component of the sum of the vectors in B is at most 1. Woeginger [17] claimed that the problem has no APTAS for dimensions greater than or equal to 2. We note that there was a slight oversight in the original proof. In this work, we give a revised proof using some additional ideas from [3,8]. In fact, we show that it is NP-hard to get an asymptotic approximation ratio better than 600599.An instance of Vector Bin Packing is called δ-skewed if every item has at most one dimension greater than δ. As a natural extension of our general d-Dimensional Vector Bin Packing result we show that for ε∈(0,12500) it is NP-hard to obtain a (1+ε)-approximation for δ-Skewed Vector Bin Packing if δ>20ε.In the Vector Bin Covering problem given a set of d-dimensional vectors from [0,1]d, the aim is to obtain a family of disjoint subsets (called bins) with the maximum cardinality such that for each bin B, each component of the sum of the vectors in B is at least 1. Using ideas similar to our Vector Bin Packing result, we show that for Vector Bin Covering there is no APTAS for dimensions greater than or equal to 2. In fact, we show that it is NP-hard to get an asymptotic approximation ratio better than 998997.

Design of Mars global longitudinal coverage constellation leveraging resonant and periodic orbits in Mars-Phobos-Deimos system

Over the last decades, the exploration of Phobos and Deimos has acquired relevance from both scientific and human missions standpoint. Both moons can play a key role on supporting the Martian Exploration program improving teleoperation capabilities and infrastructure support. The purpose of this work is to propose a different approach to the problem of global longitudinal coverage of Mars, exploiting the characteristic of natural satellites of the planet itself. The proposed constellation can be an alternative to the Mars Areostationary Orbit (MAO), in fact, three satellites equally spaced at Deimos height are enough to provide global longitudinal coverage, with a reduced cost. The main source of perturbation at areostationary height is due to the second degree, second order sectorial harmonic of Mars gravitational field (J2,2), which requires high maintenance cost for an equivalent configuration in MAO. By leveraging Lyapunov orbits in the Mars-Deimos perturbed Three Body Problem, it’s possible to achieve long term stable orbits with lower cost, as well as ballistic orbits with bounded variations. The characteristics and the performance of the constellation are analyzed, as well as the transfer orbits between the Mars-Deimos Lagrange points leveraging resonant orbits. The possibility of placing an extra satellite in an orbit around Phobos with the purpose of increasing performance is also detailed, as well as the transfer trajectory from the Deimos L3 point to a DRO orbit around Phobos.

Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis‐Hastings Warm‐Starting Algorithm

AbstractQuantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA.

Обновленческий Поместный Собор 1925 года (на материале журнала «Вестник Священного синода Православной российской церкви»)

This article deals with the problem of information coverage of the Renovationist Local Councils on the pages of the (Renovationist) journal "Bulletin of the Holy Synod of OrthodoX Churches of the USSR". Thus, the article is mainly of a source-based nature. However, the background of the restoration of the conciliar administration of the Russian Church, the problems associated with determining the nature of the local council, i.e., its powers and composition were also considered. In addition, we have highlighted the issue of reception of the institution of a local council within the framework of the Renovationist schism, whose leaders tried to give the schism a legitimate character by holding two local councils in 1923 and 1925. The appeal to the materials of the "Bulletin" allowed us to compare the goals and objectives set by the Renovationist leadership before the Third All-Russian (second Renovationist) Local Council of 1925 and its actual results.

Discrete grey wolf optimization algorithm for solving k-coverage problem in directional sensor networks with network lifetime maximization viewpoint

Unlike the traditional wireless sensor networks (WSNs) which apply omni-directional sensors, the directional sensor networks (DSNs) utilize directional sensor nodes. Each directional sensor in DSN is a self-configured in one direction and one coverage range at a same time. In critical industries, the target coverage problem in which every target should be observed by k different sensors increases the reliability and leads the fault tolerant observation. In this case, the huge amount of energy is consumed in comparison with one coverage problem. Since the business continuity in such industries strongly depends on the network lifetime, the energy management and lifetime maximization of such resource-limited networks are still of the most important challenges. To address the issue, this paper formulates the k-coverage challenge to a discrete optimization problem with the network lifespan expansion viewpoint which is an NP-Hard problem. To solve this combinatorial problem, a discrete grey wolf optimization algorithm (D-GWA) is presented. This D-GWA proposes abundant novel exploration and exploitation procedures which permutes discrete search space efficiently. In this regard, the new fitness function is also defined which steers solutions in the directions to engage sensors uniformly in different rounds. It potentially improves network lifetime because of uniform battery usage. During the course of optimization, it utilizes temperature concept of simulated annealing algorithm to running away from local trap. To verify the proposed algorithm in solving k-coverage problem in DSNs, twelve scenarios are conducted. The simulation results experimentally prove that the totally dominance of the proposed algorithm against state-of-the-arts HTOH, LA-based, GWA, and hybrid PSO-GA approaches respectively are the amount of 31.37%, 20.97%, 14.12%, and 7.93% improvement in term of network lifetime expansion. Furthermore, the behavior of D-GWA shows the high potential of scalability in the larger search space.

Performance Analysis and Testing of a Multi-Duct Orchard Sprayer

A multi-duct orchard sprayer is designed in this paper to address the problem of low droplet coverage during plant protection in walnut orchards in South Xinjiang, China. This spray comprises a base frame, a pesticide tank, an air delivery system, a copying base frame and a drive system. Effects of the sprayer structure on the flow field were simulated using computational fluid dynamics. Operation parameters were optimised using the response surface analysis and validated using a field test. The results demonstrated that five jet tubes in the simulation design could fulfil the design requirements of GB/T 32250.3-2022. The upper, middle and lower droplet coverages were 74.92%, 90.01% and 69.9%, respectively, when the sprayer’s advancing speed, the angle of jet tubes and the nozzle diameter were 0.53 m/s, 70.27° and 0.81 mm, respectively. The machine can effectively enhance the spraying efficiency and droplet coverage of each canopy during plant protection operations in the new walnut orchards of South Xinjiang, China, and provide references for designing and optimising fruit tree spraying machinery.