Advertisement

Annals of Operations Research

, Volume 18, Issue 1, pp 245–259 | Cite as

A minimum length covering subgraph of a network

  • Tae Ung Kim
  • Timothy J. Lowe
  • James E. Ward
  • Richard L. Francis
Section IV Discrete And Network Location Problems

Abstract

This paper concerns the problem of locating a central facility on a connected networkN. The network,N, could be representative of a transport system, while the central facility takes the form of a connected subgraph ofN. The problem is to locate a central facility of minimum length so that each of several demand points onN is covered by the central facility: a demand point atv i inN is covered by the central facility if the shortest path distance betweenv i and the closest point in the central facility does not exceed a parameterr i . This location problem is NP-hard, but for certain special cases, efficient solution methods are available.

Keywords

Short Path Transport System Solution Method Location Problem Minimum Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Aho, J.E. Hopcroft and J.D. Ullman,The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, MA, 1974).Google Scholar
  2. [2]
    M. Behzad, G. Chartland and L. Lesniak-Foster,Graphs and Digraphs (Wardsworth International Group, Belmont, CA, 1979).Google Scholar
  3. [3]
    O. Berman and G.Y. Handler, Optimal minimax path of a single service unit on a network to nonservice destinations, Transportation Science 21 (1987) 115.Google Scholar
  4. [4]
    M-L. Chen, R.L. Francis and T.J. Lowe, The one-center problem: exploiting block structure, Transportation Science (to appear).Google Scholar
  5. [5]
    J. Current, C. Revelle and J. Cohon, The shortest covering path problem: an application of locational constraints to network design, Journal of Regional Science 24 (1984) 161.Google Scholar
  6. [6]
    J. Current, C. Revelle and J. Cohon, The maximum covering/shortest path problem: a multiobjective network design and routing formulation, European Journal of Operational Research 21 (1985) 189.CrossRefMathSciNetGoogle Scholar
  7. [7]
    J. Current, C. Revelle and J. Cohon, The hierarchical network design problem, European Journal of Operational Research 27 (1986) 57.Google Scholar
  8. [8]
    J. Current, C. Revelle and J. Cohon, The median shortest path problem: a multiobjective approach to analyze cost vs. accessibility in the design of transport networks, Transportation Science (to appear).Google Scholar
  9. [9]
    E.W. Dijkstra, A note on two problems in connexion with graphs, Numer. Math. 1 (1959) 269.CrossRefGoogle Scholar
  10. [10]
    M.R. Gary and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman and Co., San Francisco, CA, 1979).Google Scholar
  11. [11]
    Y. Gurevich, L. Stockmeyer and U. Viskin, Solving NP-hard problems on graphs that are almost trees and an application to facility location problems, J. Assoc. Comput. Mach. 31 (1984) 459.MathSciNetGoogle Scholar
  12. [12]
    F. Harary,Graph Theory (Addison-Wesley Publishing Co., Reading, MA, 1969).Google Scholar
  13. [13]
    S.M. Hedetniemi, E.J. Cockayne and S.T. Hedetniemi, Linear algorithm for finding the Jordan center and path center of a tree, Transportation Science 15 (1981) 98.Google Scholar
  14. [14]
    T.U. Kim, T.J. Lowe, J.E. Ward and R.L. Francis, A minimal length covering subtree of a tree, Working Paper, Krannert Graduate School of Management, Purdue University, West Lafayette, IN, 1986.Google Scholar
  15. [15]
    R.K. Kincaid, T.J. Lowe and T.L. Morin, The location of central structures in trees, Comput. Opns. Res. 15 (1988) 103.CrossRefGoogle Scholar
  16. [16]
    E. Minieka, The optimal location of a path or tree in a tree network, Networks 15 (1985) 309.Google Scholar
  17. [17]
    P.J. Slater, Locating paths in a graph, Transportation Science 16 (1982) 1.Google Scholar
  18. [18]
    H. Whitney, Non-separable and planar graphs, Transactions of the American Mathematical Society 34 (1983) 339.Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1989

Authors and Affiliations

  • Tae Ung Kim
    • 1
  • Timothy J. Lowe
    • 2
  • James E. Ward
    • 2
  • Richard L. Francis
    • 3
  1. 1.Sung Kyun Kwan UniversitySeoulKorea
  2. 2.Purdue UniversityWest LafayetteU.S.A.
  3. 3.University of FloridaGainesvilleU.S.A.

Personalised recommendations