The probability-based covering algorithm(PBCA) is a new algorithm based on probability distribution. It decides, by voting, the class of the tested samples on the border of the coverage area, based on the probability ...The probability-based covering algorithm(PBCA) is a new algorithm based on probability distribution. It decides, by voting, the class of the tested samples on the border of the coverage area, based on the probability of training samples. When using the original covering algorithm(CA), many tested samples that are located on the border of the coverage cannot be classified by the spherical neighborhood gained. The network structure of PBCA is a mixed structure composed of both a feed-forward network and a feedback network. By using this method of adding some heterogeneous samples and enlarging the coverage radius,it is possible to decrease the number of rejected samples and improve the rate of recognition accuracy. Relevant computer experiments indicate that the algorithm improves the study precision and achieves reasonably good results in text classification.展开更多
Currently,the industry is experiencing an exponential increase in dealing with binary-based combinatorial problems.In this sense,metaheuristics have been a common trend in the field in order to design approaches to so...Currently,the industry is experiencing an exponential increase in dealing with binary-based combinatorial problems.In this sense,metaheuristics have been a common trend in the field in order to design approaches to solve them successfully.Thus,a well-known strategy consists in the use of algorithms based on discrete swarms transformed to perform in binary environments.Following the No Free Lunch theorem,we are interested in testing the performance of the Fruit Fly Algorithm,this is a bio-inspired metaheuristic for deducing global optimization in continuous spaces,based on the foraging behavior of the fruit fly,which usually has much better sensory perception of smell and vision than any other species.On the other hand,the Set Coverage Problem is a well-known NP-hard problem with many practical applications,including production line balancing,utility installation,and crew scheduling in railroad and mass transit companies.In this paper,we propose different binarization methods for the Fruit Fly Algorithm,using Sshaped and V-shaped transfer functions and various discretization methods to make the algorithm work in a binary search space.We are motivated with this approach,because in this way we can deliver to future researchers interested in this area,a way to be able to work with continuous metaheuristics in binary domains.This new approach was tested on benchmark instances of the Set Coverage Problem and the computational results show that the proposed algorithm is robust enough to produce good results with low computational cost.展开更多
Fractional vegetation cover(FVC)is an important parameter to measure crop growth.In studies of crop growth monitoring,it is very important to extract FVC quickly and accurately.As the most widely used FVC extraction m...Fractional vegetation cover(FVC)is an important parameter to measure crop growth.In studies of crop growth monitoring,it is very important to extract FVC quickly and accurately.As the most widely used FVC extraction method,the photographic method has the advantages of simple operation and high extraction accuracy.However,when soil moisture and acquisition times vary,the extraction results are less accurate.To accommodate various conditions of FVC extraction,this study proposes a new FVC extraction method that extracts FVC from a normalized difference vegetation index(NDVI)greyscale image of wheat by using a density peak k-means(DPK-means)algorithm.In this study,Yangfumai 4(YF4)planted in pots and Yangmai 16(Y16)planted in the field were used as the research materials.With a hyperspectral imaging camera mounted on a tripod,ground hyperspectral images of winter wheat under different soil conditions(dry and wet)were collected at 1 m above the potted wheat canopy.Unmanned aerial vehicle(UAV)hyperspectral images of winter wheat at various stages were collected at 50 m above the field wheat canopy by a UAV equipped with a hyperspectral camera.The pixel dichotomy method and DPK-means algorithm were used to classify vegetation pixels and non-vegetation pixels in NDVI greyscale images of wheat,and the extraction effects of the two methods were compared and analysed.The results showed that extraction by pixel dichotomy was influenced by the acquisition conditions and its error distribution was relatively scattered,while the extraction effect of the DPK-means algorithm was less affected by the acquisition conditions and its error distribution was concentrated.The absolute values of error were 0.042 and 0.044,the root mean square errors(RMSE)were 0.028 and 0.030,and the fitting accuracy R2 of the FVC was 0.87 and 0.93,under dry and wet soil conditions and under various time conditions,respectively.This study found that the DPK-means algorithm was capable of achieving more accurate results than the pixel dichotomy method in various soil and time conditions and was an accurate and robust method for FVC extraction.展开更多
In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain t...In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.展开更多
This paper presents a new hybrid genetic algorithm for the vertex cover problems in which scan-repair and local improvement techniques are used for local optimization. With the hybrid approach, genetic algorithms are ...This paper presents a new hybrid genetic algorithm for the vertex cover problems in which scan-repair and local improvement techniques are used for local optimization. With the hybrid approach, genetic algorithms are used to perform global exploration in a population, while neighborhood search methods are used to perform local exploitation around the chromosomes. The experimental results indicate that hybrid genetic algorithms can obtain solutions of excellent quality to the problem instances with different sizes. The pure genetic algorithms are outperformed by the neighborhood search heuristics procedures combined with genetic algorithms.展开更多
This paper describes an extremely fast polynomial time algorithm, the NOVCA (Near Optimal Vertex Cover Algorithm) that produces an optimal or near optimal vertex cover for any known undirected graph G (V, E). NOVC...This paper describes an extremely fast polynomial time algorithm, the NOVCA (Near Optimal Vertex Cover Algorithm) that produces an optimal or near optimal vertex cover for any known undirected graph G (V, E). NOVCA is based on the idea of(l) including the vertex having maximum degree in the vertex cover and (2) rendering the degree of a vertex to zero by including all its adjacent vertices. The three versions of algorithm, NOVCA-I, NOVCA-II, and NOVCA-random, have been developed. The results identifying bounds on the size of the minimum vertex cover as well as polynomial complexity of algorithm are given with experimental verification. Future research efforts will be directed at tuning the algorithm and providing proof for better approximation ratio with NOVCA compared to any available vertex cover algorithms.展开更多
Construction of Covering Arrays (CA) with minimum possible number of rows is challenging. Often the available CA have redundant combinatorial interaction that could be removed to reduce the number of rows. This pape...Construction of Covering Arrays (CA) with minimum possible number of rows is challenging. Often the available CA have redundant combinatorial interaction that could be removed to reduce the number of rows. This paper addresses the problem of removing redundancy of CA using a metaheuristic post- optimization (MPO) approach. Our approach consists of three main components: a redundancy detector (RD); a row reducer (RR); and a missing-combinations reducer (MCR). The MCR is a metaheuristic component implemented using a simulated annealing algorithm. MPO was instantiated with 21,964 CA taken from the National Institute of Standards and Technology (NIST) repository. It is a remarkable result that this instantiation of MPO has delivered 349 new upper bounds for these CA.展开更多
Climate is a critical factor affecting forest ecosystems and their capacity to produce goods and services. Effects of climate change on forests depend on ecosystem-specific factors including dimensions of climate (te...Climate is a critical factor affecting forest ecosystems and their capacity to produce goods and services. Effects of climate change on forests depend on ecosystem-specific factors including dimensions of climate (temperature, precipitation, drought, wind etc.). Available infor- mation is not sufficient to support a quantitative assessment of the eco- logical, social and economic consequences. The present study assessed shifts in forest cover types of Western Himalayan Eco-region (700-4 500 m). 100 randomly selected samples (75 for training and 25 for testing the model), genetic algorithm of rule set parameters and climatic envelopes were used to assess the distribution of five prominent forest cover types (Temperate evergreen, Tropical semi-evergreen, Temperate conifer, Sub- tropical conifer, and Tropical moist deciduous forests). Modelling was conducted for four different scenarios, current scenario, changed precipi- tation (8% increase), changed temperature (1.07℃ increase), and both changed temperature and precipitation. On increasing precipitation a downward shift in the temperate evergreen and tropical semi-evergreen was observed, while sub-tropical conifer and tropical moist-deciduous forests showed a slight upward shift and temperate conifer showed 'no shift. On increasing temperatm'e, an upward shift in all forest types was observed except sub-tropical conifer forests without significant changes. When both temperature and precipitation were changed, the actual dis- tribution was maintained and slight upward shift was observed in all the forest types except sub-tropical conifer. It is important to understand the likely impacts of the projected climate change on the forest ecosystems, so that better management and conservation strategies can be adopted for the biodiversity and forest dependent community. Knowledge of impact mechanisms also enables identification and mitigation of some of the conditions that increase vulnerability to climate change in the forest sector.展开更多
Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted n...Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.展开更多
About one third of the water needed for agriculture in the world is generated by melting snow. Snow cover, surface and ground water recharge are considered as sustainable and renewable resources. It is therefore neces...About one third of the water needed for agriculture in the world is generated by melting snow. Snow cover, surface and ground water recharge are considered as sustainable and renewable resources. It is therefore necessary to identify and study these criteria. The aim of this study is to determine the spatial and temporal distribution of snow cover in the district of the Sheshpir basin in Fars province (in south of Iran). Ground-based observation of snow covers, especially in mountainous areas, is associated with many problems due to the insufficient accuracy of optical observation, as opposed to digital observation. Therefore, GIS and remote sensing technology can be partially effective in solving this problem. Images of Landsat 5<sup>TM</sup> and Landsat 7<sup>TM</sup> satellites were used to derive snow cover maps. The images in ENVI 4.8 software were classified by using the maximum likelihood algorithm. Other spatial analyses were performed in ARC-GIS 9.3 software. The maximum likelihood method was accuracy assessed by operation points of testing. The least and the average of overall accuracy of produced maps were found to be 91% and 98%, respectively. This demonstrates that the maximum likelihood method has high performance in the classification of images. Overall snow cover and the review of terrain through the years 2008-2009 and 2009-2010 showed that snow cover begins to accumulate in November and reaches its highest magnitude in February. Finally, no trace of snow can be observed on the surface of the basin in the month of May. By average, 34% of the basin is covered in snow from November through to May.展开更多
The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with...The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.展开更多
A critical problem associated with the southern part of Nigeria is the rapid alteration of the landscape as a result of logging, agricultural practices, human migration and expansion, oil exploration, exploitation and...A critical problem associated with the southern part of Nigeria is the rapid alteration of the landscape as a result of logging, agricultural practices, human migration and expansion, oil exploration, exploitation and production activities. These processes have had both positive and negative effects on the economic and socio-political development of the country in general. The negative impacts have led not only to the degradation of the ecosystem but also posing hazards to human health and polluting surface and ground water resources. This has created the need for the development of a rapid, cost effective and efficient land use/land cover (LULC) classification technique to monitor the biophysical dynamics in the region. Due to the complex land cover patterns existing in the study area and the occasionally indistinguishable relationship between land cover and spectral signals, this paper introduces a combined use of unsupervised and supervised image classification for detecting land use/land cover (LULC) classes. With the continuous conflict over the impact of oil activities in the area, this work provides a procedure for detecting LULC change, which is an important factor to consider in the design of an environmental decision-making framework. Results from the use of this technique on Landsat TM and ETM+ of 1987 and 2002 are discussed. The results reveal the pros and cons of the two methods and the effects of their overall accuracy on post-classification change detection.展开更多
基金supported by the Fund for Philosophy and Social Science of Anhui Provincethe Fund for Human and Art Social Science of the Education Department of Anhui Province(Grant Nos.AHSKF0708D13 and 2009sk038)
文摘The probability-based covering algorithm(PBCA) is a new algorithm based on probability distribution. It decides, by voting, the class of the tested samples on the border of the coverage area, based on the probability of training samples. When using the original covering algorithm(CA), many tested samples that are located on the border of the coverage cannot be classified by the spherical neighborhood gained. The network structure of PBCA is a mixed structure composed of both a feed-forward network and a feedback network. By using this method of adding some heterogeneous samples and enlarging the coverage radius,it is possible to decrease the number of rejected samples and improve the rate of recognition accuracy. Relevant computer experiments indicate that the algorithm improves the study precision and achieves reasonably good results in text classification.
文摘Currently,the industry is experiencing an exponential increase in dealing with binary-based combinatorial problems.In this sense,metaheuristics have been a common trend in the field in order to design approaches to solve them successfully.Thus,a well-known strategy consists in the use of algorithms based on discrete swarms transformed to perform in binary environments.Following the No Free Lunch theorem,we are interested in testing the performance of the Fruit Fly Algorithm,this is a bio-inspired metaheuristic for deducing global optimization in continuous spaces,based on the foraging behavior of the fruit fly,which usually has much better sensory perception of smell and vision than any other species.On the other hand,the Set Coverage Problem is a well-known NP-hard problem with many practical applications,including production line balancing,utility installation,and crew scheduling in railroad and mass transit companies.In this paper,we propose different binarization methods for the Fruit Fly Algorithm,using Sshaped and V-shaped transfer functions and various discretization methods to make the algorithm work in a binary search space.We are motivated with this approach,because in this way we can deliver to future researchers interested in this area,a way to be able to work with continuous metaheuristics in binary domains.This new approach was tested on benchmark instances of the Set Coverage Problem and the computational results show that the proposed algorithm is robust enough to produce good results with low computational cost.
基金supported by the Beijing Natural Science Foundation,China(4202066)the Central Public-interest Scientific Institution Basal Research Fund,China(JBYWAII-2020-29 and JBYW-AII-2020-31)+1 种基金the Key Research and Development Program of Hebei Province,China(19227407D)the Technology Innovation Project Fund of Chinese Academy of Agricultural Sciences(CAAS-ASTIP2020-All)。
文摘Fractional vegetation cover(FVC)is an important parameter to measure crop growth.In studies of crop growth monitoring,it is very important to extract FVC quickly and accurately.As the most widely used FVC extraction method,the photographic method has the advantages of simple operation and high extraction accuracy.However,when soil moisture and acquisition times vary,the extraction results are less accurate.To accommodate various conditions of FVC extraction,this study proposes a new FVC extraction method that extracts FVC from a normalized difference vegetation index(NDVI)greyscale image of wheat by using a density peak k-means(DPK-means)algorithm.In this study,Yangfumai 4(YF4)planted in pots and Yangmai 16(Y16)planted in the field were used as the research materials.With a hyperspectral imaging camera mounted on a tripod,ground hyperspectral images of winter wheat under different soil conditions(dry and wet)were collected at 1 m above the potted wheat canopy.Unmanned aerial vehicle(UAV)hyperspectral images of winter wheat at various stages were collected at 50 m above the field wheat canopy by a UAV equipped with a hyperspectral camera.The pixel dichotomy method and DPK-means algorithm were used to classify vegetation pixels and non-vegetation pixels in NDVI greyscale images of wheat,and the extraction effects of the two methods were compared and analysed.The results showed that extraction by pixel dichotomy was influenced by the acquisition conditions and its error distribution was relatively scattered,while the extraction effect of the DPK-means algorithm was less affected by the acquisition conditions and its error distribution was concentrated.The absolute values of error were 0.042 and 0.044,the root mean square errors(RMSE)were 0.028 and 0.030,and the fitting accuracy R2 of the FVC was 0.87 and 0.93,under dry and wet soil conditions and under various time conditions,respectively.This study found that the DPK-means algorithm was capable of achieving more accurate results than the pixel dichotomy method in various soil and time conditions and was an accurate and robust method for FVC extraction.
基金Supported by the National Natural Science Foundation of China(11001242,11071220)
文摘In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.
基金This project was supported by the National Natural Science Foundation of China the Open Project Foundation of Comput-er Software New Technique National Key Laboratory of Nanjing University.
文摘This paper presents a new hybrid genetic algorithm for the vertex cover problems in which scan-repair and local improvement techniques are used for local optimization. With the hybrid approach, genetic algorithms are used to perform global exploration in a population, while neighborhood search methods are used to perform local exploitation around the chromosomes. The experimental results indicate that hybrid genetic algorithms can obtain solutions of excellent quality to the problem instances with different sizes. The pure genetic algorithms are outperformed by the neighborhood search heuristics procedures combined with genetic algorithms.
文摘This paper describes an extremely fast polynomial time algorithm, the NOVCA (Near Optimal Vertex Cover Algorithm) that produces an optimal or near optimal vertex cover for any known undirected graph G (V, E). NOVCA is based on the idea of(l) including the vertex having maximum degree in the vertex cover and (2) rendering the degree of a vertex to zero by including all its adjacent vertices. The three versions of algorithm, NOVCA-I, NOVCA-II, and NOVCA-random, have been developed. The results identifying bounds on the size of the minimum vertex cover as well as polynomial complexity of algorithm are given with experimental verification. Future research efforts will be directed at tuning the algorithm and providing proof for better approximation ratio with NOVCA compared to any available vertex cover algorithms.
文摘Construction of Covering Arrays (CA) with minimum possible number of rows is challenging. Often the available CA have redundant combinatorial interaction that could be removed to reduce the number of rows. This paper addresses the problem of removing redundancy of CA using a metaheuristic post- optimization (MPO) approach. Our approach consists of three main components: a redundancy detector (RD); a row reducer (RR); and a missing-combinations reducer (MCR). The MCR is a metaheuristic component implemented using a simulated annealing algorithm. MPO was instantiated with 21,964 CA taken from the National Institute of Standards and Technology (NIST) repository. It is a remarkable result that this instantiation of MPO has delivered 349 new upper bounds for these CA.
文摘Climate is a critical factor affecting forest ecosystems and their capacity to produce goods and services. Effects of climate change on forests depend on ecosystem-specific factors including dimensions of climate (temperature, precipitation, drought, wind etc.). Available infor- mation is not sufficient to support a quantitative assessment of the eco- logical, social and economic consequences. The present study assessed shifts in forest cover types of Western Himalayan Eco-region (700-4 500 m). 100 randomly selected samples (75 for training and 25 for testing the model), genetic algorithm of rule set parameters and climatic envelopes were used to assess the distribution of five prominent forest cover types (Temperate evergreen, Tropical semi-evergreen, Temperate conifer, Sub- tropical conifer, and Tropical moist deciduous forests). Modelling was conducted for four different scenarios, current scenario, changed precipi- tation (8% increase), changed temperature (1.07℃ increase), and both changed temperature and precipitation. On increasing precipitation a downward shift in the temperate evergreen and tropical semi-evergreen was observed, while sub-tropical conifer and tropical moist-deciduous forests showed a slight upward shift and temperate conifer showed 'no shift. On increasing temperatm'e, an upward shift in all forest types was observed except sub-tropical conifer forests without significant changes. When both temperature and precipitation were changed, the actual dis- tribution was maintained and slight upward shift was observed in all the forest types except sub-tropical conifer. It is important to understand the likely impacts of the projected climate change on the forest ecosystems, so that better management and conservation strategies can be adopted for the biodiversity and forest dependent community. Knowledge of impact mechanisms also enables identification and mitigation of some of the conditions that increase vulnerability to climate change in the forest sector.
基金partly supported by the National Natural Science Foundation of China(61751303,U20A2068,11771013)the Zhejiang Provincial Natural Science Foundation of China(LD19A010001)the Fundamental Research Funds for the Central Universities。
文摘Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.
文摘About one third of the water needed for agriculture in the world is generated by melting snow. Snow cover, surface and ground water recharge are considered as sustainable and renewable resources. It is therefore necessary to identify and study these criteria. The aim of this study is to determine the spatial and temporal distribution of snow cover in the district of the Sheshpir basin in Fars province (in south of Iran). Ground-based observation of snow covers, especially in mountainous areas, is associated with many problems due to the insufficient accuracy of optical observation, as opposed to digital observation. Therefore, GIS and remote sensing technology can be partially effective in solving this problem. Images of Landsat 5<sup>TM</sup> and Landsat 7<sup>TM</sup> satellites were used to derive snow cover maps. The images in ENVI 4.8 software were classified by using the maximum likelihood algorithm. Other spatial analyses were performed in ARC-GIS 9.3 software. The maximum likelihood method was accuracy assessed by operation points of testing. The least and the average of overall accuracy of produced maps were found to be 91% and 98%, respectively. This demonstrates that the maximum likelihood method has high performance in the classification of images. Overall snow cover and the review of terrain through the years 2008-2009 and 2009-2010 showed that snow cover begins to accumulate in November and reaches its highest magnitude in February. Finally, no trace of snow can be observed on the surface of the basin in the month of May. By average, 34% of the basin is covered in snow from November through to May.
文摘The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.
文摘A critical problem associated with the southern part of Nigeria is the rapid alteration of the landscape as a result of logging, agricultural practices, human migration and expansion, oil exploration, exploitation and production activities. These processes have had both positive and negative effects on the economic and socio-political development of the country in general. The negative impacts have led not only to the degradation of the ecosystem but also posing hazards to human health and polluting surface and ground water resources. This has created the need for the development of a rapid, cost effective and efficient land use/land cover (LULC) classification technique to monitor the biophysical dynamics in the region. Due to the complex land cover patterns existing in the study area and the occasionally indistinguishable relationship between land cover and spectral signals, this paper introduces a combined use of unsupervised and supervised image classification for detecting land use/land cover (LULC) classes. With the continuous conflict over the impact of oil activities in the area, this work provides a procedure for detecting LULC change, which is an important factor to consider in the design of an environmental decision-making framework. Results from the use of this technique on Landsat TM and ETM+ of 1987 and 2002 are discussed. The results reveal the pros and cons of the two methods and the effects of their overall accuracy on post-classification change detection.