Hansen, Pierre; Thisse, Jacques-François; Wendell, Richard E. Efficient points on a network. (English) Zbl 0644.90029 Networks 16, No. 4, 357-368 (1986). Summary: Properties of efficient points on a network are given. They are then used to devise (i) a linear algorithm for efficient points on a tree, (ii) an O(m log n) algorithm for the set of links common to all shortest paths between two points, and (iii) a polynomial algorithm for efficient points on a general network. Cited in 1 Document MSC: 90B05 Inventory, storage, reservoirs 90C35 Programming involving graphs or networks 68Q25 Analysis of algorithms and problem complexity 05C05 Trees 90C31 Sensitivity, stability, parametric optimization Keywords:location; multiple objective problem; efficient points on a network; linear algorithm; tree; polynomial algorithm PDFBibTeX XMLCite \textit{P. Hansen} et al., Networks 16, No. 4, 357--368 (1986; Zbl 0644.90029) Full Text: DOI References: [1] Chalmet, Eur. J. Opercitionol Res. 6 pp 117– (1981) [2] Church, Transportation Sci. 12 pp 107– (1978) [3] Dijkstra, Numerische Math. 1 pp 269– (1959) [4] and . Location on Networks. MIT Press. Cambridge. MA, 1979. [5] Hansen, Discrere Appl. Math. 2 pp 151– (1980) [6] Hansen, Ann. Discrete Math. 19 pp 201– (1984) [7] and , Fundamentals of Computer Algorithms. Pitman. London, 1978. · Zbl 0442.68022 [8] Karlsson, Discrete App. Math. 6 pp 91– (1983) [9] On a pair of dual nonlinear programs. I. Nonlinear Programming, (Ed.), North-Holland, Amsterdam, 1967, 37–54. [10] Lowe, Trans protation Sci. 12 pp 298– (1978) [11] Lowe, Management Sci. 30 pp 1346– (1984) [12] A new method for checking the consistency of precedence matrices. J. Assoc. Computing Machinery (1959) 164–172. · Zbl 0086.33202 [13] Thisse, Operations Res. 32 pp 1309– (1984) [14] and , Characterizing efficient points in location problems under the one-infinity norm. I. Locationcal Analysis of Public Fucilitirs, and (Eds.), North-Holland. Amsterdam. 1983, 413–429. [15] Wendell., AIIE Trans. 9 pp 238– (1977) · doi:10.1080/05695557708975152 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.