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Theory of Computing Systems

, Volume 64, Issue 2, pp 327–338 | Cite as

Algorithm for Online 3-Path Vertex Cover

  • Yubai Zhang
  • Zhao ZhangEmail author
  • Yishuo Shi
  • Xianyue Li
Article
  • 69 Downloads

Abstract

A vertex set C of a graph G = (V, E) is a 3-path vertex cover if every path on 3 vertices has at least one vertex in C. This paper studies the online version of the minimum 3-path vertex cover problem, in which vertices are revealed one by one, and one has to determine whether the newly revealed vertex should be chosen into the solution without knowing future information. We show that a natural algorithm has competitive ratio at most Δ, where Δ is the maximum degree of the graph. An example is given showing that the ratio is tight.

Keywords

Online algorithm 3-path vertex cover 

Notes

Acknowledgements

This research is supported by NSFC (11771013, 61751303, 11531011), the Zhejiang Provincial Natural Science Foundation of China (LD19A010001, LY19A010018), and the Fundamental Research Funds for the Central Universities (No. lzujbky-2017-163).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yubai Zhang
    • 1
  • Zhao Zhang
    • 2
    Email author
  • Yishuo Shi
    • 3
  • Xianyue Li
    • 4
  1. 1.College of MathematicsEast China University of Science and TechnologyShanghaiPeople’s Republic of China
  2. 2.College of Mathematics and Computer ScienceZhejiang Normal UniversityJinhuaPeople’s Republic of China
  3. 3.Institute of Information ScienceAcademia SinicaTaibeiTaiwan
  4. 4.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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