NETWORK-FLOW ALGORITHMS FOR LOWER-TRUNCATED TRANSVERSAL POLYMATROIDS
NETWORK-FLOW ALGORITHMS FOR LOWER-TRUNCATED TRANSVERSAL POLYMATROIDS
复制标题
下截断横向多边形的网络流算法
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
H. Imai
中科院分区：
文献类型：
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作者：
H. Imai
在本文中，我们引入了较低的截面多膜体，并为这些多膜质类药物开发了网络流类型的有效算法。较低截断的横截面多膜体包含特殊情况，如特殊情况，例如图形的循环基质，平面骨骼骨骼结构中的矩阵等。我们提出了简单而强大的定理，使我们能够解决这些多乳头形的各种组合优化问题通过网络流算法。尤其是，我们可以以非常有效的方式解决有关这些多重方法的贪婪型优化问题。作为贪婪类型的问题，我们处理了最大重量独立向量，找到主要分区和覆盖和包装的问题，并为它们提供有效的解决方案。在平面骨骼结构中，将一般算法用于较低截断的横截面多膜化学，以循环循环图形和矩形的曲线。从应用的角度来看，较低截断的横向多肌膜基本与具有内部自由度的离散系统有关，这在许多工程领域都会出现，因此本文开发的这些多肌动物的算法可提供有效的方法，可以有效地在某种程度上分析此类系统在某种系统中分析此类系统。统一的方式。
In this paper, we introduce lower-truncated transversal polymatroids, and develop efficient algorithms of network-flow type for those polymatroids. The lower-truncated transversal polymatroid contains, as special cases, a variety of useful matroids such as cycle matroids of graphs, matroids in plane skeletal structures, etc. We present simple and powerful theorems which enable us to solve various combinatorial optimization problems for those polymatroids by means of network-flow algorithms. Especially, we can solve greedy-type optimization problems concerning those polymatroids in a remarkably efficient manner. As greedy-type problems, we take up the problem of fmding a maximum-weight independent vector, that of finding the principal partition and that of covering and packing, and give efficient solutions for them. Applying general algorithms for lower-truncated transversal polymatroids to cycle matroids of graphs and matroids in plane skeletal structures, we obtain various new results. From the viewpoint of applications, lower-truncated transversal polymatroids are essentially related to discrete systems with internal degrees of freedom which arise in many fields of engineering, so that the algorithms for those polymatroids developed in this paper give efficient methods to analyze such systems in a unifying manner.