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1.
约束最小支撑树 ( C-MST)问题: 复杂性和上下界估计 总被引:1,自引:0,他引:1
本文首先建立了约束最小支撑树问题的模型 ,利用背包问题的复杂性 ,证明了该问题是 N P-完 全的 . 然后利用一个广义线性规划的对偶算法 ,对目标函数的上下界作出了估计 ,最后分析了解的平面 性质 . 相似文献
2.
Clique-Helly and hereditary clique-Helly graphs are polynomial-time recognizable. Recently, we presented a proof that the clique graph recognition problem is NP-complete [L. Alcón, L. Faria, C.M.H. de Figueiredo, M. Gutierrez, Clique graph recognition is NP-complete, in: Proc. WG 2006, in: Lecture Notes in Comput. Sci., vol. 4271, Springer, 2006, pp. 269-277]. In this work, we consider the decision problems: given a graph G=(V,E) and an integer k≥0, we ask whether there exists a subset V′⊆V with |V′|≥k such that the induced subgraph G[V′] of G is, variously, a clique, clique-Helly or hereditary clique-Helly graph. The first problem is clearly NP-complete, from the above reference; we prove that the other two decision problems mentioned are NP-complete, even for maximum degree 6 planar graphs. We consider the corresponding maximization problems of finding a maximum induced subgraph that is, respectively, clique, clique-Helly or hereditary clique-Helly. We show that these problems are Max SNP-hard, even for maximum degree 6 graphs. We show a general polynomial-time -approximation algorithm for these problems when restricted to graphs with fixed maximum degree Δ. We generalize these results to other graph classes. We exhibit a polynomial 6-approximation algorithm to minimize the number of vertices to be removed in order to obtain a hereditary clique-Helly subgraph. 相似文献
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图的路色数问题的NP-完全性 总被引:4,自引:0,他引:4
一个给定的图是否存在用r种颜色的正常Pk着色?称该问题为图的(k,r)路色数问题.本文研究其算法复杂性,并得到以下结果:对于任意给定的k,2≤k≤∞,图的(k,2)路色数问题及直径为2的图的(k,3)路色数问题都是NP-完全的;对于任意给定的k,2≤k≤∞,平面图的(k,3)路色数问题也是NP-完全的. 相似文献
5.
The consensus string problem for a metric is NP-complete 总被引:1,自引:0,他引:1
Given a set S of strings, a consensus string of S based on consensus error is a string w that minimizes the sum of the distances between w and all the strings in S. In this paper, we show that the problem of finding a consensus string based on consensus error is NP-complete when the penalty matrix is a metric. 相似文献
6.
We show how to use the split decomposition to solve some NP-hard optimization problems on graphs. We give algorithms for clique problem and domination-type problems. Our main result is an algorithm to compute a coloration of a graph using its split decomposition. Finally we show that the clique-width of a graph is bounded if and only if the clique-width of each representative graph in its split decomposition is bounded. 相似文献
7.
We consider project scheduling where the project manager’s objective is to minimize the time from when an adversary discovers the project until the completion of the project. We analyze the complexity of the problem identifying both polynomially solvable and NP-hard versions of the problem. The complexity of the problem is seen to be dependent on the nature of renewable resource constraints, precedence constraints, and the ability to crash activities in the project. 相似文献
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提出一种新的关于多维背包(Multi-dimensions Knapsack Problem,MKP)的约束替代问题,MKP是NP-完全问题,称这种约束替代方法为不等式单约束平面生成法.叙述了单约束不等平面生成算法的基本思想,证明了此方法的一些性质及化简问题后所得到的新问题MKPS与原问题MKP的等价性.最后用实例证实了这种化简方法及其有效性。 相似文献
10.
Aniekan Ebiefung 《Mathematical Programming》1995,69(1-3):255-268
We show that the Cottle—Dantzig generalized linear complementarity problem (GLCP) is equivalent to a nonlinear complementarity problem (NLCP), a piecewise linear system of equations (PLS), a multiple objective programming problem (MOP), and a variational inequalities problem (VIP). On the basis of these equivalences, we provide an algorithm for solving problem GLCP.Project partially supported by a grant from Oak Ridge Associated Universities, TN, USA. 相似文献