New Algorithms for Steiner Tree Reoptimization

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2024-05-29 DOI:10.1007/s00453-024-01243-2

Davide Bilò

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Abstract

Reoptimization is a setting in which we are given a good approximate solution of an optimization problem instance and a local modification that slightly changes the instance. The main goal is that of finding a good approximate solution of the modified instance. We investigate one of the most studied scenarios in reoptimization known as Steiner tree reoptimization. Steiner tree reoptimization is a collection of strongly \(\textsf {NP}\)-hard optimization problems that are defined on top of the classical Steiner tree problem and for which several constant-factor approximation algorithms have been designed in the last decades. In this paper we improve upon all these results by developing a novel technique that allows us to design polynomial-time approximation schemes. Remarkably, prior to this paper, no approximation algorithm better than recomputing a solution from scratch was known for the elusive scenario in which the cost of a single edge decreases. Our results are best possible since none of the problems addressed in this paper admits a fully polynomial-time approximation scheme, unless \(\textsf {P}=\textsf {NP}\)

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斯坦纳树再优化的新算法

重新优化是给定一个优化问题实例的良好近似解，并对该实例进行局部修改，使其略有变化。主要目标是找到修改后实例的良好近似解。我们研究了重新优化中研究最多的一种情况，即斯坦纳树重新优化。斯坦纳树再优化是一系列强（\textsf {NP}\）-硬优化问题的集合，这些问题定义在经典的斯坦纳树问题之上，在过去的几十年里，人们已经为这些问题设计了多种恒因子近似算法。在本文中，我们通过开发一种新技术，改进了所有这些结果，从而设计出了多项式时间近似方案。值得注意的是，在本文发表之前，对于单边成本下降这一难以捉摸的情况，还没有比从头开始重新计算解更好的近似算法。我们的结果是最有可能实现的，因为本文所涉及的问题中没有一个可以实现完全多项式时间的近似方案，除非（\textsf {P}=\textsf {NP}\)

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来源期刊

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.