Abstract
Given an undirected graph \( G=(V,E) \) and an integer \( \ell \), the Eccentricity Shortest Path (ESP) problem asks to check if there exists a shortest path P such that for every vertex \(v\in V(G)\), there is a vertex \(w\in P\) such that \(d_G(v,w)\le \ell \), where \(d_G(v,w)\) represents the distance between v and w in G. Dragan and Leitert [Theor. Comput. Sci. 2017] studied the optimization version of this problem which asks to find the minimum \(\ell \) for ESP and showed that it is NP-hard even on planar bipartite graphs with maximum degree 3. They also showed that ESP is W[2]-hard when parameterized by \( \ell \). On the positive side, Kučera and Suchý [IWOCA 2021] showed that ESP is fixed-parameter tractable (FPT) when parameterized by modular width, cluster vertex deletion set, maximum leaf number, or the combined parameters disjoint paths deletion set and \( \ell \). It was asked as an open question in the same paper, if ESP is FPT parameterized by disjoint paths deletion set or feedback vertex set. We answer these questions and obtain the following results:
-
1.
ESP is FPT when parameterized by disjoint paths deletion set, or the combined parameters feedback vertex set and \(\ell \).
-
2.
A (\(1+\epsilon \))-factor FPT approximation algorithm when parameterized by the feedback vertex set number.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bhyravarapu, S., Jana, S., Kanesh, L., Saurabh, S., Verma, S.: Parameterized algorithms for eccentricity shortest path problem (2023). http://arxiv.org/abs/2304.03233arXiv:2304.03233
Birmelé, É., de Montgolfier, F., Planche, L.: Minimum eccentricity shortest path problem: an approximation algorithm and relation with the k-laminarity problem. In: Chan, T.-H.H., Li, M., Wang, L. (eds.) COCOA 2016. LNCS, vol. 10043, pp. 216–229. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48749-6_16
Cygan, M., et al.: Parameterized Algorithms. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21275-3
Diestel, R.: Graph Theory. GTM, vol. 173. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-53622-3
Dragan, F.F., Leitert, A.: Minimum eccentricity shortest paths in some structured graph classes. In: Mayr, E.W. (ed.) WG 2015. LNCS, vol. 9224, pp. 189–202. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53174-7_14
Dragan, F.F., Leitert, A.: On the minimum eccentricity shortest path problem. Theoret. Comput. Sci. 694, 66–78 (2017)
Faudree, R.J., Gould, R.J., Jacobson, M.S., West, D.B.: Minimum degree and dominating paths. J. Graph Theor. 84(2), 202–213 (2017)
Kučera, M., Suchý, O.: Minimum eccentricity shortest path problem with respect to structural parameters. In: Flocchini, P., Moura, L. (eds.) IWOCA 2021. LNCS, vol. 12757, pp. 442–455. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-79987-8_31
Völkel, F., Bapteste, E., Habib, M., Lopez, P., Vigliotti, C.: Read networks and k-laminar graphs. arXiv preprint arXiv:1603.01179 (2016)
Funding
The first author acknowledges SERB-DST for supporting this research via grant PDF/2021/003452.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bhyravarapu, S., Jana, S., Kanesh, L., Saurabh, S., Verma, S. (2023). Parameterized Algorithms for Eccentricity Shortest Path Problem. In: Hsieh, SY., Hung, LJ., Lee, CW. (eds) Combinatorial Algorithms. IWOCA 2023. Lecture Notes in Computer Science, vol 13889. Springer, Cham. https://doi.org/10.1007/978-3-031-34347-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-031-34347-6_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-34346-9
Online ISBN: 978-3-031-34347-6
eBook Packages: Computer ScienceComputer Science (R0)