We survey results on the sequential and parallel complexity of hamiltonian path and cycle problems in various classes of digraphs which generalize tournaments. We give detailed informations on the difference in diffic...
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We survey results on the sequential and parallel complexity of hamiltonian path and cycle problems in various classes of digraphs which generalize tournaments. We give detailed informations on the difference in difficulties for these problems for the various classes as well as prove new results on hamiltonian paths starting in a specified vertex for a quite general class of digraphs. (C) 1999 Elsevier Science B.V. All rights reserved.
Max-max, max-min, min-max and min-min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the ...
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Max-max, max-min, min-max and min-min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the parameter. algorithms with O (n log n) and O (n(2)) running times are proposed for the problems with a fixed parameter and for the general problem, respectively, where n is the number of items to be packed into the knapsack. The latter algorithm determines optimal solution values for all values of the parameter in O (n log(2) n) time. The problem of deciding whether there exists a single optimal solution for all values of the numerical parameter is proved to be NP-complete.
Based on the hydrogen-helium similarity theory, the leakage experiments using helium instead of hydrogen can effectively reduce the risk of hydrogen deflagration, but the experimental results show that there is a larg...
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Based on the hydrogen-helium similarity theory, the leakage experiments using helium instead of hydrogen can effectively reduce the risk of hydrogen deflagration, but the experimental results show that there is a large difference between the concentration of hydrogen and helium in initial period of leakage base on this theory. This paper focuses on leakage experiments under turbulent conditions in enclosed spaces. Based on the hydrogen-helium similarity theory, helium is used to replace hydrogen to find out the concentration of helium at multiple leakage speeds. A comparison is made between helium concentration values and hydrogen concentration values, and a polynomial correction algorithm is used to shrink the difference. The results show that this correction method can reduce the concentration average error between the helium and the hydrogen from 14.06% to 7.94% for the Reynolds number range of 3500-9500. Therefore, a polynomial fitting algorithm based on this theory can improve the accuracy of experiment using helium instead of hydrogen.
The paper studies the problem of scheduling tasks on two machines to minimize the makespan. The tasks are assigned to the machine in advance. An incompatibility relation is defined over the tasks which forbids any two...
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The paper studies the problem of scheduling tasks on two machines to minimize the makespan. The tasks are assigned to the machine in advance. An incompatibility relation is defined over the tasks which forbids any two incompatible tasks to be processed at the same time. The problem can serve as a mathematical model for some batching problems in which the jobs are grouped in pairs on two machines. A linear-time algorithm is presented. (C) 2009 Elsevier B.V. All rights reserved.
We consider a problem of scheduling n jobs on two uniform parallel machines. For each job we are given its release date when the job becomes available for processing. All jobs have equal processing requirements. Preem...
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We consider a problem of scheduling n jobs on two uniform parallel machines. For each job we are given its release date when the job becomes available for processing. All jobs have equal processing requirements. Preemptions are allowed. The objective is to find a schedule minimizing total completion time. We suggest an O(n(3)) algorithm to solve this problem. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, we propose interior-point algorithms for P*(kappa)-linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functi...
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In this paper, we propose interior-point algorithms for P*(kappa)-linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functions. We show that if a strictly feasible starting point is available, then the new algorithm has O(1 + 2 kappa)root n log n log n mu(0)/epsilon and O(1 + 2 kappa)v n log n mu(0)/epsilon iteration complexity for large-and small-update methods, respectively. These are the best known complexity results for such methods.
Ordered graph and ordered graph isomorphism provide a natural representation of many objects in applications such as computational geometry, computer vision and pattern recognition. In the present paper we propose a c...
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Ordered graph and ordered graph isomorphism provide a natural representation of many objects in applications such as computational geometry, computer vision and pattern recognition. In the present paper we propose a coding procedure for ordered graphs that improves an earlier one based on Eulerian circuits of graphs in terms of both simplicity and computational efficiency. Using our coding approach, we show that the ordered graph isomorphism problem can be optimally solved in quadratic time, although no efficient (polynomial-bound) isomorphism algorithm for general graphs exists today. An experimental evaluation demonstrates the superior performance of the new method.
The SATISFACTORY PARTITION problem consists in deciding if it given graph has a partition of its vertex set into two nonempty parts Such that each vertex has at least as many neighbors in its part as in the other part...
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The SATISFACTORY PARTITION problem consists in deciding if it given graph has a partition of its vertex set into two nonempty parts Such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler [Partitioning a graph to satisfy all vertices, Technical report. Swiss Federal Institute of technology, Lausanne. 1998 algorithmic approach to the satisfactory graph partitioning problem, European J. Oper. Res. 125 (2000) 283-291] and further Studied by other authors but its complexity remained open until now. We prove in this paper that SATISFACTORY PARTION, as well as a variant where the parts are required to be of the same cardinality, are NP-complete. However, for graphs with maximum degree at most 4 the problem is polynormally solvable. We also study generalizations and variants of this problem where a partition into k nonempty parts (k >= 3) is requested. (c) 2006 Elsevier B.V. All rights reserved.
Since fuzzy discrete -event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of d...
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Since fuzzy discrete -event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of decentralized FDESs was introduced and an approach of constructing the safe codiagnoser to verify the safe codiagnosability was proposed. However, the complexity of constructing the safe codiagnoser of decentralized FDESs is exponential. In this paper, we present a polynomial verification. Firstly, the recognizer and the safe coverifier are constructed to recognize the prohibited strings in the illegal language and carry out safe diagnosis of decentralized FDESs, respectively. Then the necessary and sufficient condition for safe codiagnosability of decentralized FDESs is presented. In particular, an algorithm for verifying the safe codiagnosability of decentralized FDESs is proposed based on the safe coverifier. Notably, both complexities of constructing the safe coverifier and verifying the safe codiagnosability are polynomial in the numbers of fuzzy events and fuzzy states of FDESs. Finally, two examples are provided to illustrate the proposed algorithm and the derived results.
We consider the problem of scheduling activities of a project by a firm that competes with another firm that has to perform the same project. The profit that a firm gets from each activity depends on whether the firm ...
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We consider the problem of scheduling activities of a project by a firm that competes with another firm that has to perform the same project. The profit that a firm gets from each activity depends on whether the firm finishes the activity before or after its competitor. It is required to find a Nash equilibrium solution or show that no such solutions exist. We present a structural characterization of Nash equilibrium solutions, and a low order polynomial algorithm for the problem. (C) 2010 Elsevier B.V. All rights reserved.
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