Smoothed analysis of the successive shortest path algorithm

Tobias Brunsch, Kamiel Cornelissen, Bodo Manthey, Heiko Röglin

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

7 Citations (Scopus)
1 Downloads (Pure)


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
Title of host publicationProceedings of the 24th ACM-SIAM Symposium on Discrete Algorithms
EditorsS. Khanna
Place of PublicationNew Orleans, LA, USA
Number of pages10
ISBN (Print)978-1-611972-52-8
Publication statusPublished - 2013
Event24th ACM-SIAM Symposium on Discrete Algorithms 2013 - Astor Crowne Plaza Hotel, New Orleans, United States
Duration: 6 Jan 20138 Jan 2013
Conference number: 24

Publication series

NameProceedings ACM-SIAM Symposium on Discrete Algorithms
ISSN (Print)1557-9468


Conference24th ACM-SIAM Symposium on Discrete Algorithms 2013
Abbreviated titleSODA 2013
Country/TerritoryUnited States
CityNew Orleans
Internet address


  • Min-cost flow
  • Smoothed Analysis
  • Minimum-cost flow
  • 2023 OA procedure


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