通过提升树上的边来解决有卡片数量限制的根叶距离阻断问题的总和

IF 0.9 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Xiao Li, Xiucui Guan, Qiao Zhang, Xinyi Yin, Panos M. Pardalos
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引用次数: 0

摘要

物资运输网络可以描述为一棵有根树,每条边的拥堵程度都有一个权重。我们将有根树上的根叶距离总和(SRD)视为该树的整体拥塞度。因此,我们考虑通过升级边来解决有卡数限制的树上的 SRD 阻塞问题,用 (SDIPTC) 表示。它的目的是通过提升 N 条关键边的权重,使 SRD 最大化,从而使某些测量条件下的总提升成本上限值为给定值。相关的最小成本问题(MCSDIPTC)旨在以 SRD 为给定值的下限为前提,最小化总升级成本。我们开发了两种不同的规范,包括加权(l_\infty \)规范和加权瓶颈汉明距离来衡量升级成本。我们针对这两种规范下的问题(SDIPTC)提出了两种二进制搜索算法,分别只需 O(\(n\log n\)) 时间。对于问题(MCSDIPTC),我们提出了两种二进制搜索算法,在加权(l_\infty \)规范和加权瓶颈汉明距离下分别在 O(N n^2)和 O(n \log n\)时间内完成。这些问题通过它们的子问题(SDIPT)和(MCSDIPT)来解决,其中我们忽略了对升级边数量的卡片性约束。最后,我们设计了数值实验来展示这些算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

A network for the transportation of supplies can be described as a rooted tree with a weight of a degree of congestion for each edge. We take the sum of root-leaf distance (SRD) on a rooted tree as the whole degree of congestion of the tree. Hence, we consider the SRD interdiction problem on trees with cardinality constraint by upgrading edges, denoted by (SDIPTC). It aims to maximize the SRD by upgrading the weights of N critical edges such that the total upgrade cost under some measurement is upper-bounded by a given value. The relevant minimum cost problem (MCSDIPTC) aims to minimize the total upgrade cost on the premise that the SRD is lower-bounded by a given value. We develop two different norms including weighted \(l_\infty \) norm and weighted bottleneck Hamming distance to measure the upgrade cost. We propose two binary search algorithms within O(\(n\log n\)) time for the problems (SDIPTC) under the two norms, respectively. For problems (MCSDIPTC), we propose two binary search algorithms within O(\(N n^2\)) and O(\(n \log n\)) under weighted \(l_\infty \) norm and weighted bottleneck Hamming distance, respectively. These problems are solved through their subproblems (SDIPT) and (MCSDIPT), in which we ignore the cardinality constraint on the number of upgraded edges. Finally, we design numerical experiments to show the effectiveness of these algorithms.

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来源期刊
Journal of Combinatorial Optimization
Journal of Combinatorial Optimization 数学-计算机:跨学科应用
CiteScore
2.00
自引率
10.00%
发文量
83
审稿时长
6 months
期刊介绍: The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.
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