## Faster Parametric Shortest Path and Minimum Balance Algorithms (1991)

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Venue: | NETWORKS |

Citations: | 52 - 2 self |

### BibTeX

@MISC{Young91fasterparametric,

author = {Neal E. Young and Robert E. Tarjan and James B. Orlin},

title = {Faster Parametric Shortest Path and Minimum Balance Algorithms},

year = {1991}

}

### Years of Citing Articles

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### Abstract

### Citations

590 |
Fibonacci heaps and their uses in improved network optimization algorithms
- Fredman, Tarjan
- 1987
(Show Context)
Citation Context ...ters, Inc., and Prime Computer. 0 NETWORKS, Vol. 21:2 (March, 1991) c○1991 by John Wiley & Sons, Inc. 12 YOUNG, TARJAN, AND ORLIN advantage of the Fibonacci heap data structure of Fredman and Tarjan =-=[2]-=-. The second section describes the minimum mean cycle problem and how the parametric shortest path algorithm can be used to solve it. The third section describes the minimum-balance problem and an alg... |

213 |
A characterization of the minimum cycle mean in a digraph
- Karp
- 1978
(Show Context)
Citation Context ...d time for the parametric shortest path algorithm to find a minimum mean cycle is close to O(m + n log n), and that even for small graphs the algorithm is faster than the O(nm)-time algorithm of Karp =-=[6]-=-. A solution to the parametric shortest path problem is given by a sequence of trees, which our algorithm generates but does not store. The final section discusses how the trees may be implicitly stor... |

187 |
Graphs and Algorithms
- Gondran, Minoux
- 1984
(Show Context)
Citation Context ...ate the initial part of the sequence of trees in reverse. We leave open the problem of finding an initial value of the parameter in the general case. The minimum average weighted length cycle problem =-=[4]-=- is a generalization of the minimum mean cycle problem in which each edge of the graph has a (positive) weight as well as a cost. The problem is to find the cycle that minimizes the ratio of the sum o... |

143 |
Amortized computational complexity
- Tarjan
- 1985
(Show Context)
Citation Context ...TARJAN, AND ORLIN Tarjan of the Fibonacci heap data structure [2] in 1984. The advantage of the F-heap data structure is that the time taken to decrease or insert a key is O(1) in the amortized sense =-=[13]-=-. The time taken to find the minimum key or increase a key is O(log n) in the amortized sense. Although we can construct graphs yielding Θ(nm) key increases, so that storing the edge keys in an F-heap... |

89 |
Applications of path compression on balanced trees
- Tarjan
- 1979
(Show Context)
Citation Context ... a running time of Θ(nm). The total time for contraction can be reduced to O(J +n log n), where J is the number of shortest path changes, by using a variant of the union-find data structure of Tarjan =-=[12]-=-. The time for adding the partial potentials is similarly reduced, so this modification should remove the bottleneck. We have not estimated the expected running time of the modified algorithm.PARAMET... |

70 |
Finding minimum-cost circulations by canceling negative cycles
- Goldberg, Tarjan
- 1989
(Show Context)
Citation Context ... of the edges on the cycle. The average edge cost of such a cycle is called the minimum cycle mean. Solutions to this problem are needed in a minimum-cost circulation algorithm of Goldberg and Tarjan =-=[3]-=- and in a graph minimum-balancing algorithm of Schneider and Schneider [11]. The problem has been studied by Karp [6], who gave an O(nm)time dynamic programming algorithm, and by Ahuja and Orlin [1], ... |

49 | New Scaling Algorithms for the Assignment and Minimum Cycle Mean Problems
- Orlin, Ahuja
- 1988
(Show Context)
Citation Context ...n [3] and in a graph minimum-balancing algorithm of Schneider and Schneider [11]. The problem has been studied by Karp [6], who gave an O(nm)time dynamic programming algorithm, and by Ahuja and Orlin =-=[1]-=-, who gave an O( √ nm log nC)-time scaling algorithm. (Here, C is the maximum of the edge costs, which must be integers for the Ahuja-Orlin algorithm to work correctly.)8 YOUNG, TARJAN, AND ORLIN As ... |

40 |
Parametric shortest paths algorithm with an application to cyclic staffing
- Karp, Orlin
- 1981
(Show Context)
Citation Context ...c shortest path problem and an algorithm for solving it that runs in O(nm + n2 log n)-time on an n-vertex graph with m edges. The algorithm is based on an O(nm log n)-time algorithm of Karp and Orlin =-=[7]-=-, modified to take ∗ Research supported by the Hertz Foundation. † Research at Princeton University partially supported by National Science Foundation Grant DCR-8605961 and Office of Naval Research Co... |

12 |
Max-Balancing Weighted Directed Graphs and Matrix Scaling
- Schneider, Schneider
- 1991
(Show Context)
Citation Context ... to solve it. The third section describes the minimum-balance problem and an algorithm for solving it that runs in O(nm + n 2 log n)-time. The algorithm combines the method of Schneider and Schneider =-=[11]-=-, which yields a straightforward O(n 2 m)time algorithm for the problem, with the parametric shortest path algorithm. The fourth section describes the results of implementing the parametric shortest p... |

2 |
A minimum concave cost dynamic network flow problem, with an application to lot sizing
- Graves, Orlin
(Show Context)
Citation Context ...s desired, such λi and the corresponding Ti can simply be removed from the sequence. Applications of the parametric shortest path problem include the minimum concave-cost dynamic network flow problem =-=[5]-=-, matrix scaling [8, 10], and the minimum mean cycle and minimum balancing problems, discussed below. 2.1 An Inductive Method A natural method for solving the parametric shortest path problem is to pr... |

2 | Computing optimal scalings by parametric network algorithms
- Orlin, Rothblum
- 1985
(Show Context)
Citation Context ...nd the corresponding Ti can simply be removed from the sequence. Applications of the parametric shortest path problem include the minimum concave-cost dynamic network flow problem [5], matrix scaling =-=[8, 10]-=-, and the minimum mean cycle and minimum balancing problems, discussed below. 2.1 An Inductive Method A natural method for solving the parametric shortest path problem is to proceed tree by tree. That... |

1 |
Towers and cycle covers for max-balanced graphs. Unpublished manuscript
- Schneider, Schneider
- 1989
(Show Context)
Citation Context ...nd the corresponding Ti can simply be removed from the sequence. Applications of the parametric shortest path problem include the minimum concave-cost dynamic network flow problem [5], matrix scaling =-=[8, 10]-=-, and the minimum mean cycle and minimum balancing problems, discussed below. 2.1 An Inductive Method A natural method for solving the parametric shortest path problem is to proceed tree by tree. That... |