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Automation and Remote Control

, Volume 79, Issue 12, pp 2203–2216 | Cite as

A Linear Algorithm for Restructuring a Graph

  • K. Yu. Gorbunov
  • V. A. Lyubetsky
Optimization, System Analysis, and Operations Research

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.

Keywords

graph cycle chain graph transformation operation cost combinatorial problem optimization on graphs linear algorithm 

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References

  1. 1.
    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.CrossRefGoogle Scholar
  2. 2.
    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.CrossRefGoogle Scholar
  3. 3.
    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.CrossRefGoogle Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    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.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems (Kharkevich Institute)Russian Academy of SciencesMoscowRussia
  2. 2.Lomonosov State UniversityMoscowRussia

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