We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for ...We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.展开更多
In multi-component systems,the components are dependent,rather than degenerating independently,leading to changes inmaintenance schedules.In this situation,this study proposes a grouping dynamicmaintenance strategy.Co...In multi-component systems,the components are dependent,rather than degenerating independently,leading to changes inmaintenance schedules.In this situation,this study proposes a grouping dynamicmaintenance strategy.Considering the structure of multi-component systems,the maintenance strategy is determined according to the importance of the components.The strategy can minimize the expected depreciation cost of the system and divide the system into optimal groups that meet economic requirements.First,multi-component models are grouped.Then,a failure probability model of multi-component systems is established.The maintenance parameters in each maintenance cycle are updated according to the failure probability of the components.Second,the component importance indicator is introduced into the grouping model,and the optimization model,which aimed at a maximum economic profit,is established.A genetic algorithm is used to solve the non-deterministic polynomial(NP)-complete problem in the optimization model,and the optimal grouping is obtained through the initial grouping determined by random allocation.An 11-component series and parallel system is used to illustrate the effectiveness of the proposed strategy,and the influence of the system structure and the parameters on the maintenance strategy is discussed.展开更多
Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed sy...Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed systems. In general, multi-constrained path selection with or without optimization is a NP-complete problem that can not be exactly solved in polynomial time. Hence, accurate constraints-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The expected impact of such a constrained-based routing algorithm has resulted in the proposal of numerous heuristics and a few exact QoS algorithms. This paper aims to give a thorough, concise and fair evaluation of the most important multiple constraint-based QoS multicast routing algorithms known today, and it provides a descriptive overview and simulation results of these multi-constrained routing algorithms.展开更多
The single machine parallel-batch scheduling with deteriorating jobs and rejection is considered in this paper.A job is either rejected,in which a rejection penalty should be paid,or accepted and processed on the mach...The single machine parallel-batch scheduling with deteriorating jobs and rejection is considered in this paper.A job is either rejected,in which a rejection penalty should be paid,or accepted and processed on the machine.Each job’s processing time is an increasing linear function of its starting time.The machine can process any number of jobs simultaneously as a batch.The processing time of a batch is equal to the largest processing time of the jobs in the batch.The objectives are to minimize the makespan and the total weighted completion time,respectively,under the condition that the total rejection penalty cannot exceed a given upper bound Q.We show that both problems are NP-complete and present dynamic programming algorithms and fully polynomial time approximation schemes(FPTASs)for the considered problems.展开更多
Given a complete graph with vertex set X and subsets X_1, X_2,..., X_n, the problem of finding a subgraph G with minimum number of edges such that for every i = 1, 2,..., n G contains a spanning tree on X_i, arises in...Given a complete graph with vertex set X and subsets X_1, X_2,..., X_n, the problem of finding a subgraph G with minimum number of edges such that for every i = 1, 2,..., n G contains a spanning tree on X_i, arises in the design of vaccum systems. In general, this problem is NP-complete and it is proved that for n = 2 and 3 this problem is polynomial-time solvable. In this paper, we prove that for n = 4, the problem is also polynomial-time solvable and give a method to construct the corresponding graph.展开更多
Let G be an edge-colored graph. The monochromatic tree partition problem is to find the minimum number of vertex disjoint monochromatic trees to cover the all vertices of G. In the authors' previous work, it has been...Let G be an edge-colored graph. The monochromatic tree partition problem is to find the minimum number of vertex disjoint monochromatic trees to cover the all vertices of G. In the authors' previous work, it has been proved that the problem is NP-complete and there does not exist any constant factor approximation algorithm for it unless P= NP. In this paper the authors show that for any fixed integer r ≥ 5, if the edges of a graph G are colored by r colors, called an r-edge-colored graph, the problem remains NP-complete. Similar result holds for the monochromatic path (cycle) partition problem. Therefore, to find some classes of interesting graphs for which the problem can be solved in polynomial time seems interesting. A linear time algorithm for the monochromatic path partition problem for edge-colored trees is given.展开更多
In the theory of computational complexity, the travelling salesman problem is a typical one in the NP class. With the aid of a brand-new approach named “maximum-deleting method”, a fast algorithm is constructed for ...In the theory of computational complexity, the travelling salesman problem is a typical one in the NP class. With the aid of a brand-new approach named “maximum-deleting method”, a fast algorithm is constructed for it with a polynomial time of biquadrate, which greatly reduces the computational complexity. Since this problem is also NP-complete, as a corollary, P = NP is proved to be true. It indicates the crack of the well-known open problem named “P versus NP”.展开更多
In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “...In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “divide” and applied it in construction of solution space. Then, by application of a sticker based parallel algorithm using biological operations, independent set problem was resolved in polynomial time.展开更多
The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set proble...The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set problem. At first step, surface-based DNA solution space was constructed by using appropriate DNA strands. Then, by application of a DNA parallel algorithm, dominating set problem was resolved in polynomial time.展开更多
Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we ...Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we will show that an unconventional coloring scheme of the edges leads to an NP-complete problem when one intends to determine the optimal number of colors.展开更多
A new parallel algorithm is proposed for the knapsack problem where the method of divide and conquer is adopted. Based on an EREW-SIMD machine with shared memory, the proposed algorithm utilizes O(2 n/4 ) 1-ε ...A new parallel algorithm is proposed for the knapsack problem where the method of divide and conquer is adopted. Based on an EREW-SIMD machine with shared memory, the proposed algorithm utilizes O(2 n/4 ) 1-ε processors, 0≤ ε ≤1, and O(2 n/2 ) memory to find a solution for the n -element knapsack problem in time O(2 n/4 (2 n/4 ) ε) . The cost of the proposed parallel algorithm is O(2 n/2 ) , which is an optimal method for solving the knapsack problem without memory conflicts and an improved result over the past researches.展开更多
文摘We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.
基金supported by the National Natural Science Foundation of China under Grant No.12172100.
文摘In multi-component systems,the components are dependent,rather than degenerating independently,leading to changes inmaintenance schedules.In this situation,this study proposes a grouping dynamicmaintenance strategy.Considering the structure of multi-component systems,the maintenance strategy is determined according to the importance of the components.The strategy can minimize the expected depreciation cost of the system and divide the system into optimal groups that meet economic requirements.First,multi-component models are grouped.Then,a failure probability model of multi-component systems is established.The maintenance parameters in each maintenance cycle are updated according to the failure probability of the components.Second,the component importance indicator is introduced into the grouping model,and the optimization model,which aimed at a maximum economic profit,is established.A genetic algorithm is used to solve the non-deterministic polynomial(NP)-complete problem in the optimization model,and the optimal grouping is obtained through the initial grouping determined by random allocation.An 11-component series and parallel system is used to illustrate the effectiveness of the proposed strategy,and the influence of the system structure and the parameters on the maintenance strategy is discussed.
文摘Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed systems. In general, multi-constrained path selection with or without optimization is a NP-complete problem that can not be exactly solved in polynomial time. Hence, accurate constraints-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The expected impact of such a constrained-based routing algorithm has resulted in the proposal of numerous heuristics and a few exact QoS algorithms. This paper aims to give a thorough, concise and fair evaluation of the most important multiple constraint-based QoS multicast routing algorithms known today, and it provides a descriptive overview and simulation results of these multi-constrained routing algorithms.
基金Supported by the National Natural Science Foundation of China(11871213,71431004).
文摘The single machine parallel-batch scheduling with deteriorating jobs and rejection is considered in this paper.A job is either rejected,in which a rejection penalty should be paid,or accepted and processed on the machine.Each job’s processing time is an increasing linear function of its starting time.The machine can process any number of jobs simultaneously as a batch.The processing time of a batch is equal to the largest processing time of the jobs in the batch.The objectives are to minimize the makespan and the total weighted completion time,respectively,under the condition that the total rejection penalty cannot exceed a given upper bound Q.We show that both problems are NP-complete and present dynamic programming algorithms and fully polynomial time approximation schemes(FPTASs)for the considered problems.
文摘Given a complete graph with vertex set X and subsets X_1, X_2,..., X_n, the problem of finding a subgraph G with minimum number of edges such that for every i = 1, 2,..., n G contains a spanning tree on X_i, arises in the design of vaccum systems. In general, this problem is NP-complete and it is proved that for n = 2 and 3 this problem is polynomial-time solvable. In this paper, we prove that for n = 4, the problem is also polynomial-time solvable and give a method to construct the corresponding graph.
基金Supported by the National Natural Science Foundation of China,PCSIRT and the"973"Program
文摘Let G be an edge-colored graph. The monochromatic tree partition problem is to find the minimum number of vertex disjoint monochromatic trees to cover the all vertices of G. In the authors' previous work, it has been proved that the problem is NP-complete and there does not exist any constant factor approximation algorithm for it unless P= NP. In this paper the authors show that for any fixed integer r ≥ 5, if the edges of a graph G are colored by r colors, called an r-edge-colored graph, the problem remains NP-complete. Similar result holds for the monochromatic path (cycle) partition problem. Therefore, to find some classes of interesting graphs for which the problem can be solved in polynomial time seems interesting. A linear time algorithm for the monochromatic path partition problem for edge-colored trees is given.
文摘In the theory of computational complexity, the travelling salesman problem is a typical one in the NP class. With the aid of a brand-new approach named “maximum-deleting method”, a fast algorithm is constructed for it with a polynomial time of biquadrate, which greatly reduces the computational complexity. Since this problem is also NP-complete, as a corollary, P = NP is proved to be true. It indicates the crack of the well-known open problem named “P versus NP”.
文摘In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “divide” and applied it in construction of solution space. Then, by application of a sticker based parallel algorithm using biological operations, independent set problem was resolved in polynomial time.
文摘The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set problem. At first step, surface-based DNA solution space was constructed by using appropriate DNA strands. Then, by application of a DNA parallel algorithm, dominating set problem was resolved in polynomial time.
文摘Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we will show that an unconventional coloring scheme of the edges leads to an NP-complete problem when one intends to determine the optimal number of colors.
文摘A new parallel algorithm is proposed for the knapsack problem where the method of divide and conquer is adopted. Based on an EREW-SIMD machine with shared memory, the proposed algorithm utilizes O(2 n/4 ) 1-ε processors, 0≤ ε ≤1, and O(2 n/2 ) memory to find a solution for the n -element knapsack problem in time O(2 n/4 (2 n/4 ) ε) . The cost of the proposed parallel algorithm is O(2 n/2 ) , which is an optimal method for solving the knapsack problem without memory conflicts and an improved result over the past researches.