### 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 language | Undefined |
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Pages | 27-30 |

Number of pages | 4 |

Publication status | Published - 2013 |

Event | 12th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2013 - University of Twente, Enschede Duration: 21 May 2013 → 23 May 2013 Conference number: 12 http://wwwhome.math.utwente.nl/~ctw/ |

### Workshop

Workshop | 12th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2013 |
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Abbreviated title | CTW |

City | Enschede |

Period | 21/05/13 → 23/05/13 |

Internet address |

### Keywords

- EWI-23215
- Minimum-cost flow
- Smoothed Analysis
- Successive shortest path
- IR-86039

## Cite this

Brunsch, T., Röglin, H., Cornelissen, K. (Ed.), Hurink, J. L. (Ed.), & Manthey, B. (Ed.) (2013).

*Smoothed analysis of the successive shortest path algorithm*. 27-30. Paper presented at 12th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2013, Enschede, .