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

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

doi:10.1007/978-3-030-83508-8_32

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 proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

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 language	English
Title of host publication	Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings
Editors	Anna Lubiw, Mohammad Salavatipour
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	442-456
Number of pages	15
ISBN (Print)	9783030835071
DOIs	https://doi.org/10.1007/978-3-030-83508-8_32
State	Published - 1 Jan 2021
Event	17th International Symposium on Algorithms and Data Structures, WADS 2021 - Virtual, Online Duration: 9 Aug 2021 → 11 Aug 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12808 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Symposium on Algorithms and Data Structures, WADS 2021
City	Virtual, Online
Period	9/08/21 → 11/08/21

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 11 Sustainable Cities and Communities

Keywords

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

Access to Document

10.1007/978-3-030-83508-8_32

Cite this

Goodrich, M. T., Gupta, S., Khodabandeh, H., & Matias, P. (2021). How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths. In A. Lubiw, & M. Salavatipour (Eds.), Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings (pp. 442-456). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12808 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-83508-8_32

Goodrich, Michael T. ; Gupta, Siddharth ; Khodabandeh, Hadi et al. / How to Catch Marathon Cheaters : New Approximation Algorithms for Tracking Paths. Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings. editor / Anna Lubiw ; Mohammad Salavatipour. Springer Science and Business Media Deutschland GmbH, 2021. pp. 442-456 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths",

abstract = "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.",

keywords = "Approximation algorithms, Fixed-parameter tractability, Graph algorithms, Graph minor, Kernelization, Minor-free graphs, Road networks",

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Goodrich, MT, Gupta, S, Khodabandeh, H & Matias, P 2021, How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths. in A Lubiw & M Salavatipour (eds), Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12808 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 442-456, 17th International Symposium on Algorithms and Data Structures, WADS 2021, Virtual, Online, 9/08/21. https://doi.org/10.1007/978-3-030-83508-8_32

How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths. / Goodrich, Michael T.; Gupta, Siddharth; Khodabandeh, Hadi et al.
Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings. ed. / Anna Lubiw; Mohammad Salavatipour. Springer Science and Business Media Deutschland GmbH, 2021. p. 442-456 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12808 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

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Goodrich MT, Gupta S, Khodabandeh H, Matias P. How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths. In Lubiw A, Salavatipour M, editors, Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 442-456. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-83508-8_32