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Autor
Ghiyasvand Mehdi (Bu-Ali Sina University, Hamedan, Iran)
Tytuł
A New Polynomial-Time Implementation of the Out-of-Kilter Algorithm Using Minty's Lemma
Źródło
Control and Cybernetics, 2014, vol. 43, nr 1, s. 79-94, rys., bibliogr. s. 93-94
Słowa kluczowe
Programowanie matematyczne, Algorytmy
Mathematical programming, Algorithms
Uwagi
summ.
Abstrakt
It is less well known how to use the out-of-kilter idea to solve the min-cost flow problem because the generic version of the out-of-kilter algorithm runs in exponential time, although it is the sort of algorithm that computers can do easily. Ciupala (2005) presented a scaling out-of-kilter algorithm that runs in polynomial time using the shortest path computation in each phase. In this paper, we present a new polynomial time implementation of out-of-kilter idea. The algorithm uses a scaling method that is different from Ciupala's scaling method. Each phase of Ciupala's method needs a shortest path computation, while our algorithm uses Minty's lemma to transform all the out-of-kilter arcs into in-kilter arcs. When the given network is infeasible, Ciupala's algorithm does not work, but our algorithm presents some information that helps to repair the infeasible network. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej
Pełny tekst
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Bibliografia
Pokaż
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  9. GONDRAN M. and MINOUX M. (1984) Graphs and Algorithms (trans. S. Vajda). Wiley, New York.
  10. HASSIN R. (1983) The minimum cost flow problem: A unifying approach to dual algorithms and a new tree search algorithm. Mathematical Programming 25, 228-239.
  11. HOFFMAN A.J. (1960) Some recent applications of the theory of linear in- equalities to extremal combinatorial analysis. In: R. Bellman and M. Hall (eds.), Combinatorial Analysis. Proc. of Symposia in Applied Mathematics, X. American Mathematical Society, Providence, Rhode Island, 113-127.
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  14. MINTY G.J. (1966) On the Axiomatic Foundations of the Theories of Directed linear Graphs, Electrical Networks and Programming. Journal of Mathematics and Mechanics 15, 485-520.
  15. ORLIN J.B. (1993) A faster strongly polynomial minimum cost flow algorithm. Operations Research, 41, 338 350.
Cytowane przez
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ISSN
0324-8569
Język
eng
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