Abstract
We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and remove an edge from the other end. We show that this problem may be solved in linear time in trees, and is fixed-parameter tractable when parameterized either by the cyclomatic number of the input graph or by the length of the path. However, it is \(\mathsf {PSPACE}\)-complete for paths of unbounded length in graphs of bounded bandwidth.
Supported in part by NSF grants CCF-1618301 and CCF-1616248.
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
References
Ito, T., et al.: On the complexity of reconfiguration problems. Theoret. Comput. Sci. 412(12–14), 1054–1065 (2011)
Mouawad, A.E., Nishimura, N., Raman, V., Simjour, N., Suzuki, A.: On the parameterized complexity of reconfiguration problems. Algorithmica 78(1), 274–297 (2017)
Kamiński, M., Medvedev, P., Milanič, M.: Shortest paths between shortest paths. Theoret. Comput. Sci. 412(39), 5205–5210 (2011)
Bonsma, P.: The complexity of rerouting shortest paths. Theoret. Comput. Sci. 510, 1–12 (2013)
Hanaka, T., et al.: Reconfiguring spanning and induced subgraphs. In: Wang, L., Zhu, D. (eds.) COCOON 2018. LNCS, vol. 10976, pp. 428–440. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94776-1_36
De Biasi, M., Ophelders, T.: The complexity of Snake. In: Demaine, E.D., Grandoni, F. (eds.) 8th International Conference on Fun with Algorithms, FUN 2016, 8–10 June 2016, La Maddalena, Italy, vol. 49. Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 11:1–11:13 (2016)
Gupta, S., Sa’ar, G., Zehavi, M.: The parameterized complexity of motion planning for snake-like robots. Electronic preprint arxiv:1903.02445, March 2019
Nešetřil, J., de Mendez, P.O.: Bounded height trees and tree-depth. Sparsity. AC, vol. 28, pp. 115–144. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27875-4_6
Wrochna, M.: Reconfiguration in bounded bandwidth and tree-depth. J. Comput. Syst. Sci. 93, 1–10 (2018)
Hopcroft, J.E., Wong, J.K.: Linear time algorithm for isomorphism of planar graphs (preliminary report). In: Proceedings of the Sixth Annual ACM Symposium on Theory of Computing (STOC 1974), pp. 172–184 (1974)
Bodlaender, H.L.: On linear time minor tests with depth-first search. J. Algorithms 14(1), 1–23 (1993)
Fellows, M.R., Langston, M.A.: On search, decision, and the efficiency of polynomial-time algorithms. J. Comput. Syst. Sci. 49(3), 769–779 (1994)
Alon, N., Yuster, R., Zwick, U.: Color-coding. J. ACM 42(4), 844–856 (1995)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Demaine, E.D. et al. (2019). Reconfiguring Undirected Paths. In: Friggstad, Z., Sack, JR., Salavatipour, M. (eds) Algorithms and Data Structures. WADS 2019. Lecture Notes in Computer Science(), vol 11646. Springer, Cham. https://doi.org/10.1007/978-3-030-24766-9_26
Download citation
DOI: https://doi.org/10.1007/978-3-030-24766-9_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-24765-2
Online ISBN: 978-3-030-24766-9
eBook Packages: Computer ScienceComputer Science (R0)