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Locating a Point of Minimum Variance on Triangular Graphs

Author

Listed:
  • Rex K. Kincaid

    (College of William and Mary, Williamsburg, Virginia)

  • Oded Z. Maimon

    (Tel Aviv University, Israel)

Abstract

In this note the convexity of the variance measure for triangular graphs is established, and an expression for the point that minimizes the variance on an edge is given. A transformation of triangular graphs into trees provides an efficient means to implement these properties via a postorder search of a tree. The result is a linear time algorithm that determines a point of minimum variance for any triangular graph whose edge lengths satisfy the triangle inequality.

Suggested Citation

  • Rex K. Kincaid & Oded Z. Maimon, 1989. "Locating a Point of Minimum Variance on Triangular Graphs," Transportation Science, INFORMS, vol. 23(3), pages 216-219, August.
    • Handle: RePEc:inm:ortrsc:v:23:y:1989:i:3:p:216-219
    DOI: 10.1287/trsc.23.3.216
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    Cited by:

    1. Bélanger, V. & Ruiz, A. & Soriano, P., 2019. "Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles," European Journal of Operational Research, Elsevier, vol. 272(1), pages 1-23.
    2. Cruz Lopez-de-los-Mozos, M. & Mesa, Juan A., 2001. "The maximum absolute deviation measure in location problems on networks," European Journal of Operational Research, Elsevier, vol. 135(1), pages 184-194, November.

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