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一个图增广问题的NC算法
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作者 屈婉玲 袁崇义 《北京大学学报(自然科学版)》 CAS CSCD 北大核心 1998年第5期694-699,共6页
随着并行计算和网络技术的广泛应用,图论中的k-边连通性增广问题受到越来越多的注意。早期的研究已经证明一般性的增广问题是NP难的,但对它的某些子问题,即当k=2,E0(G的补图的边集)中所有边的权都相等时,存在着多项式... 随着并行计算和网络技术的广泛应用,图论中的k-边连通性增广问题受到越来越多的注意。早期的研究已经证明一般性的增广问题是NP难的,但对它的某些子问题,即当k=2,E0(G的补图的边集)中所有边的权都相等时,存在着多项式时间的顺序算法。本文针对上述子问题,在SIMDPRAMCRCW并行计算模型上给出了一个O(logn)时间,O(n+m)处理器的NC算法。 展开更多
关键词 增广问题 k-边连通性 NC算法
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限制性多源点偏心距增广问题
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作者 李建平 蔡力健 +1 位作者 李陈筠然 潘鹏翔 《运筹学学报》 CSCD 北大核心 2022年第1期60-68,共9页
给定一个赋权图G=(V,E;w,c)以及图G的一个支撑子图G_(1)=(V,E_(1)),这里源点集合S={s_(1),s_(2),…,s_(k)}?V,权重函数w:E→R^(+),费用函数c:E\E_(1)→Z^(+)和一个正整数B,本文考虑两类限制性多源点偏心距增广问题,具体叙述如下:(1)限... 给定一个赋权图G=(V,E;w,c)以及图G的一个支撑子图G_(1)=(V,E_(1)),这里源点集合S={s_(1),s_(2),…,s_(k)}?V,权重函数w:E→R^(+),费用函数c:E\E_(1)→Z^(+)和一个正整数B,本文考虑两类限制性多源点偏心距增广问题,具体叙述如下:(1)限制性多源点最小偏心距增广问题是要寻找一个边子集E_(2)■E\E_(1),满足约束条件c(E_(2))≤B,目标是使得子图G_(1)∪E_(2)上源点集S中顶点偏心距的最小值达到最小;(2)限制性多源点最大偏心距增广问题是要寻找一个边子集E_(2)■E\E_(1),满足约束条件c(E_(2))≤B,目标是使得子图G_(1)∪E_(2)上源点集S中顶点偏心距的最大值达到最小。本文设计了两个固定参数可解的常数近似算法来分别对上述两类问题进行求解。 展开更多
关键词 组合优化 偏心距 增广问题 参数复杂性 固定参数可解的近似算法
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Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization 被引量:6
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作者 梁昔明 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2001年第2期167-172,共6页
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi... Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems. 展开更多
关键词 modified augmented Lagrange multiplier methods chemical engineering optimization large-scale non- linear constrained minimization numerical experiment
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Bottleneck Analysis of the Minimum Cost Problem for the Generalized Network Based on Augmented Forest Structure
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作者 江永亨 王军 金以慧 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2003年第1期62-67,共6页
The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented ... The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented forest structure, then augments flows on the negative cost graphs until the optimal revolution is gained. Bottleneck structure is presented after analyzing the augmented forest structure. The negative cost augmented graphs are constructed with the bottleneck structure. The arcs that block the negative cost augmented graph are the elements of the bottleneck. The bottleneck analysis for the generalized circulation problem, the minimum circulation problem and the circulation problem are discussed respectively as the basal problems, then that for MCPGN is achieved. An example is presented at the end. 展开更多
关键词 BOTTLENECK augmented forest minimum cost problem
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