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Locating Central Paths in a Graph

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  • Peter J. Slater

    (Sandia National Laboratories, Albuquerque, New Mexico)

Abstract

Concepts which measure the centrality of a vertex in a graph (eccentricity, distance and branch weight) are extended to paths in a graph. Locating paths with minimum eccentricity and distance, respectively, may be viewed as multicenter and multimedian problems, respectively, where the facilities are located on vertices that must constitute a path. The third problem is to find a path P in a graph for which the number of vertices in the largest component of G - P is minimized. The relationships among these concepts are studied. Most of the results presented are for trees, and, in particular, linear algorithms for finding paths in trees of minimum eccentricity and of minimum branch weight are presented. These problems arise in determining a “most accessible” linear route in a network according to several plausible criteria.

Suggested Citation

  • Peter J. Slater, 1982. "Locating Central Paths in a Graph," Transportation Science, INFORMS, vol. 16(1), pages 1-18, February.
    • Handle: RePEc:inm:ortrsc:v:16:y:1982:i:1:p:1-18
    DOI: 10.1287/trsc.16.1.1
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    Cited by:

    1. Timothy J. Niblett & Richard L. Church, 2016. "The Shortest Covering Path Problem," International Regional Science Review, , vol. 39(1), pages 131-151, January.
    2. Alessandra Cornaro & Daniele Grechi, 2023. "Evaluation of Railway Systems: A Network Approach," Sustainability, MDPI, vol. 15(10), pages 1-19, May.
    3. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    4. Mulder, H.M. & Pelsmajer, M.J. & Reid, K.B., 2006. "Generalized centrality in trees," Econometric Institute Research Papers EI 2006-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Becker, Ronald I. & Lari, Isabella & Scozzari, Andrea, 2007. "Algorithms for central-median paths with bounded length on trees," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1208-1220, June.
    6. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    7. Mehdi Zaferanieh & Jafar Fathali, 2012. "Finding a core of a tree with pos/neg weight," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 147-160, October.
    8. Matsypura, Dmytro & Veremyev, Alexander & Pasiliao, Eduardo L. & Prokopyev, Oleg A., 2023. "Finding the most degree-central walks and paths in a graph: Exact and heuristic approaches," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1021-1036.
    9. Contreras, Ivan & Fernández, Elena, 2012. "General network design: A unified view of combined location and network design problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 680-697.
    10. H K Smith & G Laporte & P R Harper, 2009. "Locational analysis: highlights of growth to maturity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 140-148, May.
    11. Justo Puerto & Federica Ricca & Andrea Scozzari, 2018. "Extensive facility location problems on networks: an updated review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 187-226, July.
    12. Pascual Fernández & Blas Pelegrín & José Fernández, 1998. "Location of paths on trees with minimal eccentricity and superior section," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 223-246, December.
    13. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    14. Mehrdad Moshtagh & Jafar Fathali & James MacGregor Smith & Nezam Mahdavi-Amiri, 2019. "Finding an optimal core on a tree network with M/G/c/c state-dependent queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 115-142, February.

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