Abstract
We give an O(n)-time algorithm for the minimum cost flow problem over an undirected one-tree with n vertices. A one-tree is a spanning tree with one additional edge.
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References
P. Bloomfield and W.L. Steiger, Least Absolute Deviation, Theory, Application, and Algorithms(Birkhauser, 1983)
M. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest, and R.E. Tarjan, Time bounds for selection, Computer and System Sciences 7 (1972) 448–461.
V. Chvatal, Linear Programming ( W.H. Freeman and Co., 1983 ).
M.E. Dyer, Linear time algorithms for two- and three-variable linear programs, SIAM J. Comput. 13 (1984) 31–45.
J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency for network flow problem, J. ACM 19 (1972) 248–264.
Z. Galil and E. Tardos, An O(n 2 (m + n log n)log n) min-cost flow algorithm, Proc. 27th Annual Sympos. of Found, of Comp. Sci. (1986) 1–9.
A.V. Goldberg and R.E. Tarjan, Solving minimum cost flow problem by successive approximation, Proc. 19th ACM Sympos. on the Theory of Computing (1987) 7–18.
A.V. Goldberg and R.E. Tarjan, Finding minimum-cost circulation by canceling negative cycles, Proc. 20th ACM Sympos. on the Theory of Computing (1988) 388–397.
M.D. Grigoriadis, An efficient implementation of the network simplex method, Mathematical Programming Study 26 (1986) 83–111.
M. Held and R. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138–1162.
N. Megiddo, Linear-time algorithms for linear programming in R3 and related problems, SIAM J. Comput. 12 (1983) 759–776.
J. Orlin, A faster strongly polynomial minimum cost flow algorithm, Proc. 20th ACM Sympos. on the Theory of Computing (1988) 377–387.
E. Tardos, A strongly polynomial minimum cost circulation algorithm, Combinatorica, 5 (1985) 247–255.
M. Werman, S. Peleg, R. Melter, and T.Y. Kong, Bipartite graph matching for points on a line or a circle, Journal of Algorithms 7 (1986) 277–284.
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© 1995 Kluwer Academic Publishers
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Kalantari, B., Kalantari, I. (1995). A Linear-Time Algorithm for Minimum Cost Flow on Undirected One-Trees. In: Colbourn, C.J., Mahmoodian, E.S. (eds) Combinatorics Advances. Mathematics and Its Applications, vol 329. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3554-2_13
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DOI: https://doi.org/10.1007/978-1-4613-3554-2_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3556-6
Online ISBN: 978-1-4613-3554-2
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