Abstract
We propose an algorithm, linear in both running time and memory, that constructs a sequence of operations that transform any given directed graph with degree of any vertex at most two to any other given graph of the same type with minimal total cost. This sequence is called the shortest one. We allow four standard operations of re-gluing graphs with equal cost and two more additional operations of inserting and deleting a connected section of edges that also have equal cost. We prove that the algorithm finds a minimum with this restriction on the costs.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Gorbunov, K.Yu. and Lyubetsky, V.A., A Linear Algorithm for the Shortest Transformation of Graphs with Different Operation Costs, J. Commun. Technol. Electron., 2017, vol. 62, no. 6, pp. 653–662.
Lyubetsky, V.A., Gershgorin, R.A., Seliverstov, A.V., and Gorbunov, K.Yu., Algorithms for Reconstruction of Chromosomal Structures, BMC Bioinformatics, 2016, vol. 17, pp. 40.1–40.23.
Lyubetsky, V.A., Gershgorin, R.A., and Gorbunov, K.Yu., Chromosome Structures: Reduction of Certain Problems with Unequal Gene Content and Gene Paralogs to Integer Linear Programming, BMC Bioinformatics, 2017, vol. 18, pp. 537.1–537.18.
Braga, M.D.V. and Stoye, J., Sorting Linear Genomes with Rearrangements and Indels, IEEE/ACM Trans. Computat. Biol. Bioinformatics, 2015, vol. 12, no. 3, pp. 1–13.
Yin, Z., Tang, J., Schaeffer, S.W., and Bader, D.A., Exemplar or Matching: Modeling DCJ Problems with Unequal Content Genome Data, J. Combinatorial Optimization, 2016, vol. 32, no. 4, pp. 1165–1181.
Gorbunov, K.Yu. and Lyubetsky, V.A., Linear Algorithm for Minimal Rearrangement of Structures, Probl. Inform. Transmiss., 2017, vol. 53, no 1, pp. 55–72.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.Yu. Gorbunov, V.A. Lyubetsky, 2018, published in Avtomatika i Telemekhanika, 2018, No. 12, pp. 124–141.
Rights and permissions
About this article
Cite this article
Gorbunov, K.Y., Lyubetsky, V.A. A Linear Algorithm for Restructuring a Graph. Autom Remote Control 79, 2203–2216 (2018). https://doi.org/10.1134/S0005117918120093
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117918120093