### Finding minimum-cost circulations by canceling negative cyclesFinding minimum-cost circulations by canceling negative cycles

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 Author Goldberg, Andrew V. ♦ Tarjan, Robert E. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1989 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract A classical algorithm for finding a minimum-cost circulation consists of repeatedly finding a residual cycle of negative cost and $\textit{canceling}$ it by pushing enough flow around the cycle to saturate an arc. We show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm. This gives a very simple strongly polynomial algorithm that uses no scaling. A variant of the algorithm that uses dynamic trees runs in $&Ogr;(\textit{nm}(log$ $\textit{n})min{log(\textit{nC}),$ $\textit{m}$ log $\textit{n}})$ time on a network of $\textit{n}$ vertices, $\textit{m}$ arcs, and arc costs of maximum absolute value $\textit{C}.$ This bound is comparable to those of the fastest previously known algorithms. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1989-10-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 36 Issue Number 4 Page Count 14 Starting Page 873 Ending Page 886

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Source: ACM Digital Library