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On locating path‐ or tree‐shaped facilities on networks

par Hakimi, Shabnam Louis;Schmeichel, Edward;Labbé, Martine
Référence Networks, 23, 6, page (543-555)
Publication Publié, 1993

Article révisé par les pairs

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Résumé :

The study of “optimally” locating on a network a single facility of a given total length in the form of a path or a tree was initiated by several authors. We extend these results to the problem of locating p (≥1) such facilities. We will consider “center”, “median”, “max eccentricity”, and “max distance sum” location type problems for p = 1 or p > 1, for general networks and for tree networks, whether a facility contains partial arcs or not, and whether a facility is path‐shaped or tree‐shaped. These cases lead to 64 problems. We will determine the algorithmic complexity of virtually all these problems. We conclude with a result that may be viewed as a generalization of the p‐Median theorem. © 1993 by John Wiley & Sons, Inc. Copyright © 1993 Wiley Periodicals, Inc., A Wiley Company