Connected graph partitioning with aggregated and non‐aggregated gap objective functions
IF 1.6
4区 计算机科学
Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE
引用次数: 0
Abstract
This article deals with the problem of partitioning a graph into connected components by optimizing some balancing objective functions related to the vertex weights. Objective functions based on the gap or range of the partition's components, that is, the difference between the maximum and minimum weight of a vertex in the component, have been already introduced in the literature. Here we introduce the notion of aggregated gap, defined as the sum of the differences between the weights of the vertices and the minimum weight of a vertex in the component. We study new connected ‐partitioning problems whose objective is a function of the components' aggregated gap, and give NP‐hardness results for these problems on general graphs. Mathematical programming formulations are proposed for these problems adopting flow‐based constraints for modeling connectivity in a partition. Even if they are introduced for the new aggregated gap problems, such formulations are rather general and apply also to the classical non‐aggregated gap problems. Extensive computational tests, both for aggregated and non‐aggregated gap problems, are performed on a set of squared grids and randomly generated graphs with up to 120 vertices, and a number of components ranging from 2 to 9. In our experiments, we test several alternative formulations for our problems providing a comparative analysis of their performance.具有聚集和非聚集间隙目标函数的连通图划分
本文通过优化一些与顶点权重相关的平衡目标函数，处理了将图划分为连通分量的问题。基于分割分量的间隙或范围的目标函数，即分量中一个顶点的最大和最小权值之差，已经在文献中被引入。在这里，我们引入了聚合间隙的概念，定义为顶点的权重与组件中一个顶点的最小权重之差的总和。我们研究了新的连通划分问题，其目标是组件的聚集间隙的函数，并给出了这些问题在一般图上的NP -硬度结果。针对这些问题，提出了数学规划公式，采用基于流的约束对分区中的连通性进行建模。即使它们被引入到新的聚集间隙问题，这样的公式是相当普遍的，也适用于经典的非聚集间隙问题。对于聚集和非聚集的间隙问题，在一组方形网格和随机生成的图形上执行了大量的计算测试，这些图形具有多达120个顶点，以及一些从2到9的组件。在我们的实验中，我们为我们的问题测试了几种可供选择的配方，并对它们的性能进行了比较分析。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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来源期刊
Networks
工程技术-计算机：硬件
CiteScore
4.40
自引率
9.50%
发文量
46
审稿时长
12 months
期刊介绍：
Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context.
The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics.
Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally efficient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without significant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.
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