Purpose–Over the past decade,the cost of product development has increased drastically,and this is due to the inability of most enterprises to locate suitable and optimal collaborators for knowledge sharing.Neverthel...Purpose–Over the past decade,the cost of product development has increased drastically,and this is due to the inability of most enterprises to locate suitable and optimal collaborators for knowledge sharing.Nevertheless,knowledge sharing is a mechanism that helps people find the best collaborators with relevant knowledge.Hence,a new approach for locating optimal collaborators with relevant knowledge is needed,which couldhelp enterprisein reducingcost andtime ina knowledge-sharingenvironment.Thepaper aimsto discuss these issues.Design/methodology/approach–One unique challenge in the domain of knowledge sharing is that collaborators do not possess the same number of events resident in the knowledge available for sharing.In this paper,the authors present a new approach for locating optimal collaborators in knowledge-sharing environment using the combinatorial algorithm(CA-KSE).Findings–The proposed pattern-matching approach implemented in Java is considered efficient for solving the issue peculiar to collaboration in knowledge-sharing domain.The authors benchmarked the proposed approach with its semi-global pairwise alignment and global alignment counterparts through scores comparison and the receiver operating characteristic curve.The results obtained from the comparisons showedthat CA-KSEis a perfect test havinganarea undercurveof 0.9659,comparedto the other approaches.Research limitations/implications–The paper has proposed an efficient algorithm,which is considered better than related methods,for matching several collaborators(more than two)in KS environment.The method could be deployed in medical field for gene analysis,software organizations for distributed development and academics for knowledge sharing.Originality/value–One sign of strength of this approach,compared to most sequence alignment approaches that can only match two collaborators at a time,is that it can match several collaborators at a faster rate.展开更多
The subsea production system is a vital equipment for offshore oil and gas production.The control system is one of the most important parts of it.Collecting and processing the signals of subsea sensors is the only way...The subsea production system is a vital equipment for offshore oil and gas production.The control system is one of the most important parts of it.Collecting and processing the signals of subsea sensors is the only way to judge whether the subsea production control system is normal.However,subsea sensors degrade rapidly due to harsh working environments and long service time.This leads to frequent false alarm incidents.A combinatorial reasoning-based abnormal sensor recognition method for subsea production control system is proposed.A combinatorial algorithm is proposed to group sensors.The long short-term memory network(LSTM)is used to establish a single inference model.A counting-based judging method is proposed to identify abnormal sensors.Field data from an offshore platform in the South China Sea is used to demonstrate the effect of the proposed method.The results show that the proposed method can identify the abnormal sensors effectively.展开更多
To address the problem of identifying multiple types of additives in lubricating oil,a method based on midinfrared spectral band selection using the eXtreme Gradient Boosting(XGBoost)algorithm combined with the ant co...To address the problem of identifying multiple types of additives in lubricating oil,a method based on midinfrared spectral band selection using the eXtreme Gradient Boosting(XGBoost)algorithm combined with the ant colony optimization(ACO)algorithm is proposed.The XGBoost algorithm was used to train and test three additives,T534(alkyl diphenylamine),T308(isooctyl acid thiophospholipid octadecylamine),and T306(trimethylphenol phosphate),separately,in order to screen for the optimal combination of spectral bands for each additive.The ACO algorithm was used to optimize the parameters of the XGBoost algorithm to improve the identification accuracy.During this process,the support vector machine(SVM)and hybrid bat algorithms(HBA)were included as a comparison,generating four models:ACO-XGBoost,ACO-SVM,HBA-XGboost,and HBA-SVM.The results showed that all four models could identify the three additives efficiently,with the ACO-XGBoost model achieving 100%recognition of all three additives.In addition,the generalizability of the ACO-XGBoost model was further demonstrated by predicting a lubricating oil containing the three additives prepared in our laboratory and a collected sample of commercial oil currently in use。展开更多
A hybrid carrier(HC) scheme based on weighted-type fractional Fourier transform(WFRFT) has been proposed recently.While most of the works focus on HC scheme's inherent characteristics, little attention is paid to...A hybrid carrier(HC) scheme based on weighted-type fractional Fourier transform(WFRFT) has been proposed recently.While most of the works focus on HC scheme's inherent characteristics, little attention is paid to the WFRFT modulation recognition.In this paper, a new theory is provided to recognize the WFRFT modulation based on higher order cumulants(HOC). First, it is deduced that the optimal WFRFT received order can be obtained through the minimization of 4 th-order cumulants, C_(42). Then, a combinatorial searching algorithm is designed to minimize C_(42).Finally, simulation results show that the designed scheme has a high recognition rate and the combinatorial searching algorithm is effective and reliable.展开更多
It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optima...It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.展开更多
The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to pro...The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.展开更多
In the first part of this- paper, three generalizations of arrangement graph A.,k of [1], namely Bn,k, Cn,k and Dn,k , are introduced. We prove that all the three classes of graphs are vertex symmetric, two of them ar...In the first part of this- paper, three generalizations of arrangement graph A.,k of [1], namely Bn,k, Cn,k and Dn,k , are introduced. We prove that all the three classes of graphs are vertex symmetric, two of them are edge symmetric. They have great faulty tolerance and high connectivity. We give the diameters of B..k and Cn,k, the Hamiltonian cycle of Cn,k and Hamiltonian path of B.,k. We list several open problems, one of them related to the complexity of sorting algorithm on the arrangement graphs. All these graphs can be thought as generalizations of star graph but are more flexible so that they can be considered as new interconnection network topologies. In the second part of this paper, we provide other four classes of combinatorial graphes, Chn , Cyn, Zhn and Zyn. Many good properties of them, such as high node--connectivity, node symmetry, edge symmetry, diameter, ets., are shown in this paper.展开更多
Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution pr...Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results:In this paper,we review the theoretical framework and assumptions over which the clonal reconstruction problem is formulated.We formally define the problem and then discuss the complexity and solution space of the problem.Various methods have been proposed to find the phylogeny that best explains the observed data.We categorize these methods based on the type of input data that they use(space-resolved or time-resolved),and also based on their computational formulation as either combinatorial or probabilistic.It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem.Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction.We briefly review the existing algorithms and their relationships.Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions:In this review,we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data,review existing algorithms and catergorize them according to their problem formulation and solution approaches.We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed.We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.展开更多
In this paper, we present a novel, dynamic collaboration cloud platform in which a Combinatorial Auction(CA)-based market model enables the platform to run effectively. The platform can facilitate expense reduction ...In this paper, we present a novel, dynamic collaboration cloud platform in which a Combinatorial Auction(CA)-based market model enables the platform to run effectively. The platform can facilitate expense reduction and improve the scalability of the cloud, which is divided into three layers: The user-layer receives requests from end-users, the auction-layer matches the requests with the cloud services provided by the Cloud Service Provider(CSP), and the CSP-layer forms a coalition to improve serving ability to satisfy complex requirements of users.In fact, the aim of the coalition formation is to find suitable partners for a particular CSP. However, identifying a suitable combination of partners to form the coalition is an NP-hard problem. Hence, we propose approximation algorithms for the coalition formation. The Breadth Traversal Algorithm(BTA) and Revised Ant Colony Algorithm(RACA) are proposed to form a coalition when bidding for a single cloud service in the auction. The experimental results show that RACA outperforms the BTA in bid price. Other experiments were conducted to evaluate the impact of the communication cost on coalition formation and to assess the impact of iteration times for the optimal bidding price. In addition, the performance of the market model was compared to the existing CA-based model in terms of economic efficiency.展开更多
An incidence of a graph G is a vertex-edge pair(v,e)such that v is incidence with e.A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences(u,e)and(v,f)get disti...An incidence of a graph G is a vertex-edge pair(v,e)such that v is incidence with e.A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences(u,e)and(v,f)get distinct colors if and only if they conflict each other,i.e.,(i)u=v,(ii)uv is e or f,or(iii)there is a vertex w such that uw=e and vw=f.The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number.A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once.In this paper,we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree△is either 2△or 2△+1 unless the graph is a cycle on three vertices,and moreover,all outer-1-planar graphs with conflict-free incidence chromatic number 2△or 2△+1 are completely characterized.An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.展开更多
The investigation of genetic differences among humans has given evidence thatmutations in DNA sequences are responsible for some genetic diseases. The most common mutation isthe one that involves only a single nucleot...The investigation of genetic differences among humans has given evidence thatmutations in DNA sequences are responsible for some genetic diseases. The most common mutation isthe one that involves only a single nucleotide of the DNA sequence, which is called a singlenucleotide polymorphism (SNP). As a consequence, computing a complete map of all SNPs occurring inthe human populations is one of the primary goals of recent studies in human genomics. Theconstruction of such a map requires to determine the DNA sequences that from all chromosomes. Indiploid organisms like humans, each chromosome consists of two sequences called haplotypes.Distinguishing the information contained in both haplotypes when analyzing chromosome sequencesposes several new computational issues which collectively form a new emerging topic of ComputationalBiology known as Haplotyping. This paper is a comprehensive study of some new combinatorialapproaches proposed in this research area and it mainly focuses on the formulations and algorithmicsolutions of some basic biological problems. Three statistical approaches are briefly discussed atthe end of the paper.展开更多
The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a...The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitive automorphism groups of linear spaces. In two of these cases the group may be imprimitive on points, that is, the group leaves invariant a nontrivial partition of the point set. In the first of these cases the group is almost simple with point-transitive simple socle, and may or may not be point-primitive, while in the second case the group has a non-trivial point-intransitive normal subgroup and hence is definitely point-imprimitive. The theory presented here focuses on point-imprimitive groups. As a non-trivial application a classification is given of the point-imprimitive, line-transitive groups, and the corresponding linear spaces, for which the greatest common divisor gcd(k, v - 1) ≤ 8, where v is the number of points, and k is the line size. Motivation for this classification comes from a result of Weidong Fang and Huffing Li in 1993, that there are only finitely many non-trivial point-imprimitive, linetransitive linear spaces for a given value of gcd(k, v - 1). The classification strengthens the classification by Camina and Mischke under the much stronger restriction k ≤ 8: no additional examples arise. The paper provides the backbone for future computer-based classifications of point-imprimitive, line- transitive linear spaces with small parameters. Several suggestions for further investigations are made.展开更多
文摘Purpose–Over the past decade,the cost of product development has increased drastically,and this is due to the inability of most enterprises to locate suitable and optimal collaborators for knowledge sharing.Nevertheless,knowledge sharing is a mechanism that helps people find the best collaborators with relevant knowledge.Hence,a new approach for locating optimal collaborators with relevant knowledge is needed,which couldhelp enterprisein reducingcost andtime ina knowledge-sharingenvironment.Thepaper aimsto discuss these issues.Design/methodology/approach–One unique challenge in the domain of knowledge sharing is that collaborators do not possess the same number of events resident in the knowledge available for sharing.In this paper,the authors present a new approach for locating optimal collaborators in knowledge-sharing environment using the combinatorial algorithm(CA-KSE).Findings–The proposed pattern-matching approach implemented in Java is considered efficient for solving the issue peculiar to collaboration in knowledge-sharing domain.The authors benchmarked the proposed approach with its semi-global pairwise alignment and global alignment counterparts through scores comparison and the receiver operating characteristic curve.The results obtained from the comparisons showedthat CA-KSEis a perfect test havinganarea undercurveof 0.9659,comparedto the other approaches.Research limitations/implications–The paper has proposed an efficient algorithm,which is considered better than related methods,for matching several collaborators(more than two)in KS environment.The method could be deployed in medical field for gene analysis,software organizations for distributed development and academics for knowledge sharing.Originality/value–One sign of strength of this approach,compared to most sequence alignment approaches that can only match two collaborators at a time,is that it can match several collaborators at a faster rate.
基金supported by the National Key Research and Development Program of China (No.2022YFC2806102)the National Natural Science Foundation of China (No.52171287,52325107)+3 种基金High-tech Ship Research Project of Ministry of Industry and Information Technology (No.2023GXB01-05-004-03,No.GXBZH2022-293)the Science Foundation for Distinguished Young Scholars of Shandong Province (No.ZR2022JQ25)the Taishan Scholars Project (No.tsqn201909063)the Fundamental Research Funds for the Central Universities (No.24CX10006A)。
文摘The subsea production system is a vital equipment for offshore oil and gas production.The control system is one of the most important parts of it.Collecting and processing the signals of subsea sensors is the only way to judge whether the subsea production control system is normal.However,subsea sensors degrade rapidly due to harsh working environments and long service time.This leads to frequent false alarm incidents.A combinatorial reasoning-based abnormal sensor recognition method for subsea production control system is proposed.A combinatorial algorithm is proposed to group sensors.The long short-term memory network(LSTM)is used to establish a single inference model.A counting-based judging method is proposed to identify abnormal sensors.Field data from an offshore platform in the South China Sea is used to demonstrate the effect of the proposed method.The results show that the proposed method can identify the abnormal sensors effectively.
基金the Beijing Natural Science Foundation(Grant No.2232066)the Open Project Foundation of State Key Laboratory of Solid Lubrication(Grant LSL-2212).
文摘To address the problem of identifying multiple types of additives in lubricating oil,a method based on midinfrared spectral band selection using the eXtreme Gradient Boosting(XGBoost)algorithm combined with the ant colony optimization(ACO)algorithm is proposed.The XGBoost algorithm was used to train and test three additives,T534(alkyl diphenylamine),T308(isooctyl acid thiophospholipid octadecylamine),and T306(trimethylphenol phosphate),separately,in order to screen for the optimal combination of spectral bands for each additive.The ACO algorithm was used to optimize the parameters of the XGBoost algorithm to improve the identification accuracy.During this process,the support vector machine(SVM)and hybrid bat algorithms(HBA)were included as a comparison,generating four models:ACO-XGBoost,ACO-SVM,HBA-XGboost,and HBA-SVM.The results showed that all four models could identify the three additives efficiently,with the ACO-XGBoost model achieving 100%recognition of all three additives.In addition,the generalizability of the ACO-XGBoost model was further demonstrated by predicting a lubricating oil containing the three additives prepared in our laboratory and a collected sample of commercial oil currently in use。
基金supported by the National Natural Science Foundation of China(6127125061571460)
文摘A hybrid carrier(HC) scheme based on weighted-type fractional Fourier transform(WFRFT) has been proposed recently.While most of the works focus on HC scheme's inherent characteristics, little attention is paid to the WFRFT modulation recognition.In this paper, a new theory is provided to recognize the WFRFT modulation based on higher order cumulants(HOC). First, it is deduced that the optimal WFRFT received order can be obtained through the minimization of 4 th-order cumulants, C_(42). Then, a combinatorial searching algorithm is designed to minimize C_(42).Finally, simulation results show that the designed scheme has a high recognition rate and the combinatorial searching algorithm is effective and reliable.
基金supported by the National Natural Science Foundation of China(6107901361079014+4 种基金61403198)the National Natural Science Funds and Civil Aviaiton Mutual Funds(U1533128U1233114)the Programs of Natural Science Foundation of China and China Civil Aviation Joint Fund(60939003)the Natural Science Foundation of Jiangsu Province in China(BK2011737)
文摘It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.
文摘The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.
文摘In the first part of this- paper, three generalizations of arrangement graph A.,k of [1], namely Bn,k, Cn,k and Dn,k , are introduced. We prove that all the three classes of graphs are vertex symmetric, two of them are edge symmetric. They have great faulty tolerance and high connectivity. We give the diameters of B..k and Cn,k, the Hamiltonian cycle of Cn,k and Hamiltonian path of B.,k. We list several open problems, one of them related to the complexity of sorting algorithm on the arrangement graphs. All these graphs can be thought as generalizations of star graph but are more flexible so that they can be considered as new interconnection network topologies. In the second part of this paper, we provide other four classes of combinatorial graphes, Chn , Cyn, Zhn and Zyn. Many good properties of them, such as high node--connectivity, node symmetry, edge symmetry, diameter, ets., are shown in this paper.
文摘Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results:In this paper,we review the theoretical framework and assumptions over which the clonal reconstruction problem is formulated.We formally define the problem and then discuss the complexity and solution space of the problem.Various methods have been proposed to find the phylogeny that best explains the observed data.We categorize these methods based on the type of input data that they use(space-resolved or time-resolved),and also based on their computational formulation as either combinatorial or probabilistic.It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem.Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction.We briefly review the existing algorithms and their relationships.Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions:In this review,we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data,review existing algorithms and catergorize them according to their problem formulation and solution approaches.We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed.We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.
基金supported by the National Natural Science Foundation of China (Nos. 61070133, 61170201, and 61472344)the Collegiate Natural Science Foundation of Jiangsu Province (Grant No. 11KJD520011)+1 种基金Six talent peaks project in Jiangsu Province (No. 2011-DZXX-032)the Scientific Research Foundation of Graduate School of Jiangsu Province (No. CXZZ13 0901)
文摘In this paper, we present a novel, dynamic collaboration cloud platform in which a Combinatorial Auction(CA)-based market model enables the platform to run effectively. The platform can facilitate expense reduction and improve the scalability of the cloud, which is divided into three layers: The user-layer receives requests from end-users, the auction-layer matches the requests with the cloud services provided by the Cloud Service Provider(CSP), and the CSP-layer forms a coalition to improve serving ability to satisfy complex requirements of users.In fact, the aim of the coalition formation is to find suitable partners for a particular CSP. However, identifying a suitable combination of partners to form the coalition is an NP-hard problem. Hence, we propose approximation algorithms for the coalition formation. The Breadth Traversal Algorithm(BTA) and Revised Ant Colony Algorithm(RACA) are proposed to form a coalition when bidding for a single cloud service in the auction. The experimental results show that RACA outperforms the BTA in bid price. Other experiments were conducted to evaluate the impact of the communication cost on coalition formation and to assess the impact of iteration times for the optimal bidding price. In addition, the performance of the market model was compared to the existing CA-based model in terms of economic efficiency.
基金supported by the Research Funds for the Central Universities(No.QTZX22053)the National Natural Science Foundation of China(No.11871055)。
文摘An incidence of a graph G is a vertex-edge pair(v,e)such that v is incidence with e.A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences(u,e)and(v,f)get distinct colors if and only if they conflict each other,i.e.,(i)u=v,(ii)uv is e or f,or(iii)there is a vertex w such that uw=e and vw=f.The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number.A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once.In this paper,we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree△is either 2△or 2△+1 unless the graph is a cycle on three vertices,and moreover,all outer-1-planar graphs with conflict-free incidence chromatic number 2△or 2△+1 are completely characterized.An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.
文摘The investigation of genetic differences among humans has given evidence thatmutations in DNA sequences are responsible for some genetic diseases. The most common mutation isthe one that involves only a single nucleotide of the DNA sequence, which is called a singlenucleotide polymorphism (SNP). As a consequence, computing a complete map of all SNPs occurring inthe human populations is one of the primary goals of recent studies in human genomics. Theconstruction of such a map requires to determine the DNA sequences that from all chromosomes. Indiploid organisms like humans, each chromosome consists of two sequences called haplotypes.Distinguishing the information contained in both haplotypes when analyzing chromosome sequencesposes several new computational issues which collectively form a new emerging topic of ComputationalBiology known as Haplotyping. This paper is a comprehensive study of some new combinatorialapproaches proposed in this research area and it mainly focuses on the formulations and algorithmicsolutions of some basic biological problems. Three statistical approaches are briefly discussed atthe end of the paper.
基金Supported by Australian Research Council(Grant Nos. DP0557587 and DP0209706)The fifth author is supported by Australian Research Council Federation Fellowship FF0776186The sixth author is partly supported by the NSF of Guangdong Province
文摘The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitive automorphism groups of linear spaces. In two of these cases the group may be imprimitive on points, that is, the group leaves invariant a nontrivial partition of the point set. In the first of these cases the group is almost simple with point-transitive simple socle, and may or may not be point-primitive, while in the second case the group has a non-trivial point-intransitive normal subgroup and hence is definitely point-imprimitive. The theory presented here focuses on point-imprimitive groups. As a non-trivial application a classification is given of the point-imprimitive, line-transitive groups, and the corresponding linear spaces, for which the greatest common divisor gcd(k, v - 1) ≤ 8, where v is the number of points, and k is the line size. Motivation for this classification comes from a result of Weidong Fang and Huffing Li in 1993, that there are only finitely many non-trivial point-imprimitive, linetransitive linear spaces for a given value of gcd(k, v - 1). The classification strengthens the classification by Camina and Mischke under the much stronger restriction k ≤ 8: no additional examples arise. The paper provides the backbone for future computer-based classifications of point-imprimitive, line- transitive linear spaces with small parameters. Several suggestions for further investigations are made.