Smoothed analysis of the successive shortest path algorithm

Tobias Brunsch, Kamiel Cornelissen, Johann L. Hurink, Bodo Manthey, Heiko Röglin

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Abstract

The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that both the problem and the algorithms are well understood. However, some of the algorithms' running times observed in empirical studies contrast the running times obtained by worst-case analysis not only in the order of magnitude but also in the ranking when compared to each other. For example, the Successive Shortest Path (SSP) algorithm, which has an exponential worst-case running time, seems to outperform the strongly polynomial Minimum-Mean Cycle Canceling algorithm. To explain this discrepancy, we study the SSP algorithm in the framework of smoothed analysis and establish a bound of $O(mn \phi (m + n \log n))$ for its smoothed running time. This shows that worst-case instances for the SSP algorithm are not robust and unlikely to be encountered in practice.
Original languageEnglish
Pages27-30
Number of pages4
Publication statusPublished - 2013
Event12th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2013 - University of Twente, Enschede
Duration: 21 May 201323 May 2013
Conference number: 12
http://wwwhome.math.utwente.nl/~ctw/

Workshop

Workshop12th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2013
Abbreviated titleCTW
CityEnschede
Period21/05/1323/05/13
Internet address

Keywords

  • Minimum-cost flow
  • Smoothed analysis
  • Successive shortest path

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  • Smoothed Analysis of the Successive Shortest Path Algorithm

    Brunsch, T., Cornelissen, K., Manthey, B., Röglin, H. & Rösner, C., 2015, In: SIAM journal on computing. 44, 6, p. 1798-1819 22 p.

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    6 Citations (Scopus)
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  • Smoothed analysis of the successive shortest path algorithm

    Brunsch, T., Cornelissen, K., Manthey, B. & Röglin, H., 2013, Proceedings of the 24th ACM-SIAM Symposium on Discrete Algorithms. Khanna, S. (ed.). New Orleans, LA, USA: SIAM, p. 1180-1189 10 p. (Proceedings ACM-SIAM Symposium on Discrete Algorithms; vol. 2013, no. 24).

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