Abstract
The paper “Cycles in generalized networks” [2], which appeared in WG 2002, claims that the single source generalized shortest path problem SGSP can be solved in O(nm log n). This is incorrect. The fastest known algorithms take O(n 2 m log n) time. Below we briefly describe the problem and discuss which of our results hold.
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References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice Hall, Englewood Cliffs (1993)
Brandenburg, F.J.: Cycles in generalized networks. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 47–56. Springer, Heidelberg (2002)
Oldham, J.D.: Combinatorial approximation algorithms for generalized flow problems. J. Algorithms 38, 135–168 (2001)
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Brandenburg, F.J. (2003). Erratum: Cycles in Generalized Networks. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_33
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DOI: https://doi.org/10.1007/978-3-540-39890-5_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20452-7
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