How heavy independent sets help to find arborescences with many leaves in DAGs

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2023-08-01 DOI:10.1016/j.jcss.2023.02.006

Cristina G. Fernandes , Carla N. Lintzmayer

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引用次数: 1

Abstract

Trees with many leaves have applications for broadcasting a message to all recipients simultaneously. Internal nodes of a broadcasting tree require more expensive technology to forward the messages received. We address a problem that captures the main goal: finding spanning trees with few internal nodes in a given network. The Maximum Leaf Spanning Arborescence problem consists of, given a directed graph D, finding a spanning arborescence of D, if one exists, with the maximum number of leaves. This problem is NP-hard in general and MaxSNP-hard in the rooted directed acyclic graphs class. This paper explores a relationship between Maximum Leaf Spanning Arborescence in rooted directed acyclic graphs and maximum weight set packing. The latter problem is related to independent sets on particular classes of intersection graphs. Exploiting this relation, we derive a 7/5-approximation for Maximum Leaf Spanning Arborescence on rooted directed acyclic graphs, improving on the previous 3/2-approximation.

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重独立集如何帮助在dag中找到具有许多叶片的乔木

具有许多叶子的树具有同时向所有接收者广播消息的应用程序。广播树的内部节点需要更昂贵的技术来转发接收到的消息。我们解决了一个抓住主要目标的问题：在给定的网络中找到内部节点很少的生成树。在给定有向图D的情况下，最大叶生成树状图问题包括找到具有最大叶数的D的生成树状图（如果存在）。这个问题一般是NP难的，在根有向无环图类中是MaxSNP难的。本文研究了根有向无环图的最大展叶树期和最大权集填充之间的关系。后一个问题与特定类交集图上的独立集有关。利用这个关系，我们得到了根有向无环图上最大叶展树期的7/5近似，改进了以前的3/2近似。

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

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.