How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths

Michael T. Goodrich, Siddharth Gupta, Hadi Khodabandeh, Pedro Matias

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Given an undirected graph, G, and vertices, s and t in G, the tracking paths problem is that of finding the smallest subset of vertices in G whose intersection with any s-t path results in a unique sequence. This problem is known to be NP-complete and has applications to animal migration tracking and detecting marathon course-cutting, but its approximability is largely unknown. In this paper, we address this latter issue, giving novel algorithms having approximation ratios of (1 + ϵ), O(lg OPT) and O(lg n), for H-minor-free, general, and weighted graphs, respectively. We also give a linear kernel for H-minor-free graphs.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings
EditorsAnna Lubiw, Mohammad Salavatipour
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages15
ISBN (Print)9783030835071
StatePublished - 1 Jan 2021
Event17th International Symposium on Algorithms and Data Structures, WADS 2021 - Virtual, Online
Duration: 9 Aug 202111 Aug 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12808 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Symposium on Algorithms and Data Structures, WADS 2021
CityVirtual, Online


  • Approximation algorithms
  • Fixed-parameter tractability
  • Graph algorithms
  • Graph minor
  • Kernelization
  • Minor-free graphs
  • Road networks

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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