An Exact Polynomial Algorithm for the Outerplanar Facility Location Problem with Improved Time Complexity

  • Edward GimadiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10716)


The Unbounded Facility Location Problem on outerplanar graphs is considered. The algorithm with time complexity \( O(n m^3)\) was known for solving this problem, where \( n\) is the number of vertices, \( m\) is the number of possible plant locations. Using some properties of maximal outerplanar graphs (binary 2-trees) and the existence of an optimal solution with a family of centrally-connected service areas, the recurrence relations are obtained allowing to design an algorithm which can solve the problem in \( O(n m^{2.5})\) time.


Outerplanar graph Exact algoritm Time complexity Dynamic programming 



The author was supported by the Russian Science Foundation, project no. 16-11-10041.


  1. 1.
    Ageev, A.A.: Graphs, matrices and the simple plant location problem (in Russian). Upravlyaemye Sistemy 29, 3–12 (1989)MathSciNetGoogle Scholar
  2. 2.
    Ageev, A.A.: A polynomial algorithm for solving the location problem on a series-parallel network (in Russian). Upravlyaemye Sistemy 30, 3–6 (1990)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Billionet, A., Costa, M.-C.: Solving the uncapacitated plant location problem on trees. Discrete Appl. Math. 49(1–3), 51–59 (1994)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Gadegaard, S.L.: Discrete Location Problems. A Ph.D. dissertation, 150 p. Aarhus University Department of Economics and Business Economics (2016)Google Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979). 338 pzbMATHGoogle Scholar
  6. 6.
    Gimadi, E.K.: An efficient algorithm for solving plant location problem with service regions connected with respect to an acyclic network (in Russian). Upravlyaemye Sistemy 23, 12–23 (1983)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Gimadi, E.K.: The problem of location on a network with centrally connected service areas (in Russian). Upravlyaemye Sistemy 25, 38–47 (1984)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Hassin, R., Tamir, A.: Efficient algorithm for optimization and selection on series-parallel graphs. SIAM J. Algebraic Discrete Methods 7(3), 379–389 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kolen, A.: Solving covering problems and the uncapacitated plant location on the trees. Eur. J. Oper. Res. 12(3), 266–278 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Laporte, G., Nickel, S., da Gama, F.S. (eds.): Location Science. Springer, Cham (2015). 644 p.zbMATHGoogle Scholar
  11. 11.
    Mirchandani, P.B., Francis, R.L. (eds.): Discrete Location Theory. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York/Chichester/Brisbane/Toronto/Singapore (1990). 555 pGoogle Scholar
  12. 12.
    Trubin, V.A.: An efficient algorithm for plant locating on trees (in Russian). Dokl. AN SSSR 231(3), 547–550 (1976)Google Scholar
  13. 13.
    Ulukan, Z., Demircioglu, E.: A survey of discrete facility location problems. Int. J. Soc. Behav. Educ. Econ. Bus. Ind. Eng. 9(7), 2487–2492 (2015)Google Scholar
  14. 14.
    Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM J. Comput. 11(2), 298–313 (1982)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations