共查询到19条相似文献,搜索用时 970 毫秒
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关于整数向量卷积的一个算法的时间复杂度 总被引:2,自引:1,他引:1
众所周知,两个n维整数向量循环卷积的常规算法(即按定义计算)的时间复杂度为O(n~2),现在已有时间复杂度为O(nlog_2n)的快速算法,[1]中提出一个新算法,称其时间复杂度为O(n),因而是最佳的。 本文首先指出[1]的错误原因,再根据算法分析理论得出[1]中算法的时间复杂度不低于O(n~2log_2n),因而比常规算法的运算量还大。 相似文献
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《数学理论与应用》2017,(2)
分支降阶被广泛用来求解NP-Hard问题,该技术的核心思想是将原问题分解成若干个子问题并递归求解这些子问题,但是用来分析算法时间复杂度的常规分析技术不够精确,无法得到较好的时间复杂度.本文设计了一个基于分支降阶的递归算法求解加权最大团问题,对于提出的精确算法,首先运用常规技术对该算法进行时间复杂度分析,得出其时间复杂度为O(1.4656~np(n)),其中n代表图中结点总个数,p(n)代表n的多项式函数;然后运用加权分治技术对原算法进行时间复杂度分析,将该算法的时间复杂性由原来的O(1.4656~np(n))降为O(1.3765~np(n)).研究结果表明运用加权分治技术能够得到较为精确的时间复杂度. 相似文献
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本文提出一并行算法求解具有优个约束以及n个非负有界变量的瓶颈资源分配问题,若有m台处理机,在一定条件下该并行算法的复杂度为O(n(n+logm))。 相似文献
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岳中亮 《数学的实践与认识》2006,36(3):185-189
将动态规划中的一维背包问题推广到了n维,并利用模糊数为工具,在模糊环境下给出了n维背包问题的最优解,最后通过实例说明该方法的简便、有效和实用性. 相似文献
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《TOP》1986,1(1):139-160
Summary In this paper, we describe computationally efficient procedures for identifying all maximal cliques and non-dominated selected
subsets of extensions of minimal covers and alternates that are implied by single 0–1 knapsack constraints. The induced inequalities
are satisfied by and 0–1 feasible solution to the knapsack constraint, but are tipically violated by fractional solutions.
In addition, the procedures described here are used in conjunction with other constraints to further tighten LP relaxations
of 0–1 programs. The complexity of the procedures isO(n).
Part of this work has been done while the author was at IBM Research, T.J. Watson Research Center, NY, USA. 相似文献
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研究了可分离二次背包问题的一种直接算法.此类背包问题的目标函数是二次的,且含有严格的一次项,其不等式约束是线性的.给出所求模型的一般形式,经过预处理该模型,最终归为求解两类问题(P1)和(P2).重点是求解(P2)问题的最优解,通过分析(P2)问题的结构特点,假设固定一次项后问题的最优解和相应不等式的拉格朗日乘子已求出,通过比较拉格朗日乘子和(P2)问题的一次项系数来调节λ的大小,从而求出(P2)问题的最优解.对于(P1)问题,改进了Bretthauer和Shetty给出的算法(Bretthauer K M,Shetty B.A pegging algorithm for the nonlinear resource allocation problem.Computers and Operations Research,2002,29(5):505-527).此算法的计算复杂性为O(n).数值算例表明,将这种固定变量算法和文中的定理5结合起来,能够快速有效地求解此类更一般的二次背包问题. 相似文献
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Roberto Cominetti Walter F. Mascarenhas Paulo J. S. Silva 《Mathematical Programming Computation》2014,6(2):151-169
We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after $O(n)$ iterations with overall arithmetic complexity $O(n^2)$ . Numerical experiments show that in practice the method converges in a small number of iterations with overall linear complexity, and is faster than the state-of-the-art algorithms based on median finding, variable fixing, and secant techniques. 相似文献
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《European Journal of Operational Research》2006,175(3):1577-1587
In this paper we consider the practical implementation of the disaggregated simplicial decomposition (DSD) algorithm for the traffic assignment problem. It is a column generation method that at each step has to solve a huge number of quadratic knapsack problems (QKP). We propose a Newton-like method to solve the QKP when the quadratic functional is convex but not necessarily strictly. Our O(n) algorithm does not improve the complexity of the current methods but extends them to a more general case and is better suited for reoptimization and so a good option for the DSD algorithm. It also allows the solution of many QKP’s simultaneously in a vectorial or parallel way. 相似文献
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Summary In this brief note we present a correction of the Propositions 1 and 5 for proving the O(n) complexity of the algorithms described in [Dietrich et al. (1993)] for identifying maximal cliques and non-dominated covers
from extensions of consecutive minimal covers and alternates implied by 0–1 knapsack constraints. 相似文献
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In this short note we obtain the full set of inequalities that define the convex hull of a 0–1 knapsack constraint presented
in Weismantel (1997). For that purpose we use our O(n) procedures for identifying maximal cliques and non-dominated extensions
of consecutive minimal covers and alternates, as well as our schemes for coefficient increase based tightening cover induced
inequalities and coefficient reduction based tightening general 0–1 knapsack constraints. 相似文献
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关于矩阵乘法的一个改进算法的时间复杂度 总被引:2,自引:0,他引:2
两个n阶非负整数方阵相乘,常规算法的时间复杂度为O(n3),文献[1]提出一个“运算次数”为O(n2)的“最佳”算法,文献[2]对此算法做了进一步研究,提出三种改进策略.本文根据算法分析理论,得出改进后的算法的时间复杂度仍不低于O(n3logn),因而其阶仍高于常规算法的运算量的阶. 相似文献
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关于矩阵乘法的一个算法的时间复杂度 总被引:4,自引:1,他引:3
两个n阶非负整数方阵相乘,常规算法的时间复杂度为O(n3),文献[1]提出一个“运算次数”为O(n2)的“最佳”算法,本文根据算法分析理论得出此算法的时间复杂度不低于O(n3log2n),因而比常规算法的运算量还大. 相似文献
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This paper considers a general class of continuous, nonlinear, and nonseparable knapsack problems, special cases of which
arise in numerous operations and financial contexts. We develop important properties of optimal solutions for this problem
class, based on the properties of a closely related class of linear programs. Using these properties, we provide a solution
method that runs in polynomial time in the number of decision variables, while also depending on the time required to solve
a particular one-dimensional optimization problem. Thus, for the many applications in which this one-dimensional function
is reasonably well behaved (e.g., unimodal), the resulting algorithm runs in polynomial time. We next develop a related solution
approach to a class of continuous, nonlinear, and nonseparable multiple-choice knapsack problems. This algorithm runs in polynomial
time in both the number of variables and the number of variants per item, while again dependent on the complexity of the same
one-dimensional optimization problem as for the knapsack problem. Computational testing demonstrates the power of the proposed
algorithms over a commercial global optimization software package. 相似文献