Constant factor approximation for tracking paths and fault tolerant feedback vertex set

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2023-02-01 DOI:10.1016/j.disopt.2022.100756

Václav Blažej, Pratibha Choudhary, Dušan Knop, Jan Matyáš Křišťan, Ondřej Suchý, Tomáš Valla

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引用次数: 0

Abstract

Consider a vertex-weighted graph $G$ with a source $s$ and a target $t$ . Tracking Paths requires finding a minimum weight set of vertices (trackers) such that the sequence of trackers in each path from $s$ to $t$ is unique. In this work, we derive a factor 6-approximation algorithm for Tracking Paths in weighted graphs and a factor 4-approximation algorithm if the input is unweighted. This is the first constant factor approximation for this problem. While doing so, we also study approximation of the closely related r-Fault Tolerant Feedback Vertex Set problem. There, for a fixed integer $r$ and a given vertex-weighted graph $G$ , the task is to find a minimum weight set of vertices intersecting every cycle of $G$ in at least $r + 1$ vertices. We give a factor $O (r)$ approximation algorithm for r-Fault Tolerant Feedback Vertex Set if $r$ is a constant.

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跟踪路径的常因子逼近与容错反馈顶点集

考虑具有源s和目标t的顶点加权图G。跟踪路径需要找到顶点（跟踪器）的最小权重集，使得从s到t的每条路径中的跟踪器序列是唯一的。在这项工作中，我们导出了加权图中跟踪路径的因子6近似算法，以及如果输入是未加权的，则导出因子4近似算法。这是这个问题的第一个常数因子近似。在这样做的同时，我们还研究了密切相关的r容错反馈顶点集问题的逼近。在那里，对于固定整数r和给定的顶点加权图G，任务是在至少r+1个顶点中找到与G的每个循环相交的顶点的最小权重集。如果r是常数，我们给出了r容错反馈顶点集的因子O（r）近似算法。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.