## Negative-Cycle Detection Algorithms (1996)

Venue: | MATHEMATICAL PROGRAMMING |

Citations: | 46 - 5 self |

### BibTeX

@ARTICLE{Cherkassky96negative-cycledetection,

author = {Boris V. Cherkassky and Andrew V. Goldberg},

title = {Negative-Cycle Detection Algorithms},

journal = {MATHEMATICAL PROGRAMMING},

year = {1996},

volume = {85},

pages = {349--363}

}

### Years of Citing Articles

### OpenURL

### Abstract

We study the problem of finding a negative length cycle in a network. An algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy. We study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations. One of our discoveries is that a cycle detection strategy of Tarjan greatly improves practical performance of a classical shortest path algorithm, making it competitive with the fastest known algorithms on a wide range of problems. As a part of our study, we develop problem families for testing negative cycle algorithms.

### Citations

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Flows in Networks
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(Show Context)
Citation Context ...tive cycle problem is the problem of finding a negative length cycle in a network or proving that there are none (see e.g. [15]). The problem is closely related to the shortest path problem (see e.g. =-=[1, 7, 16, 18, 19, 20]-=-) of finding shortest path distances in a network with no negative cycles. The negative cycle problem comes up both directly, for example in currency arbitrage, and as a subproblem in algorithms for o... |

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(Show Context)
Citation Context ... the author was visiting NEC Research Institute, Inc. 1 Introduction The negative cycle problem is the problem of finding a negative length cycle in a network or proving that there are none (see e.g. =-=[15]-=-). The problem is closely related to the shortest path problem (see e.g. [1, 7, 16, 18, 19, 20]) of finding shortest path distances in a network with no negative cycles. The negative cycle problem com... |

325 |
On a routing problem
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(Show Context)
Citation Context ...tive cycle problem is the problem of finding a negative length cycle in a network or proving that there are none (see e.g. [15]). The problem is closely related to the shortest path problem (see e.g. =-=[1, 7, 16, 18, 19, 20]-=-) of finding shortest path distances in a network with no negative cycles. The negative cycle problem comes up both directly, for example in currency arbitrage, and as a subproblem in algorithms for o... |

142 | Shortest path algorithms: Theory and experimental evaluation
- Cherkassky, Goldberg, et al.
- 1996
(Show Context)
Citation Context ...aph has a negative cycle, the distance labels maintained by the labeling method (with no cycle detection) will get arbitrarily negative. Most experimental studies of shortest path algorithms, such as =-=[2, 5, 8, 17]-=-, were conducted on graphs with no negative cycles. In this paper we study the practical performance of algorithms for the negative cycle problem. We also show that a cycle detection strategy of Tarja... |

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The shortest path through a maze
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(Show Context)
Citation Context ...tive cycle problem is the problem of finding a negative length cycle in a network or proving that there are none (see e.g. [15]). The problem is closely related to the shortest path problem (see e.g. =-=[1, 7, 16, 18, 19, 20]-=-) of finding shortest path distances in a network with no negative cycles. The negative cycle problem comes up both directly, for example in currency arbitrage, and as a subproblem in algorithms for o... |

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Application of the simplex method to a transportation problem
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(Show Context)
Citation Context ...nation of the Bellman--Ford--Moore algorithm and a subtree-disassembly strategy for cycle detection. We also study several new algorithm variations. We develop a version of the network simplex method =-=[4] optimized-=- specifically for the negative cycle problem. We note that a simple modification of Tarjan's algorithm gives the "ideal" version of the Bellman--Ford--Moore algorithm and study this version.... |

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Algorithms for Network Programming
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(Show Context)
Citation Context ...ing the subtree and applying labeling operations to the tree arcs. We implement this tree traversal procedure by maintaining an in-order list of tree nodes, as in many network simplex codes. See e.g. =-=[13]-=-. At every step, a generic network simplex algorithm for shortest paths finds an arc (u; v) with negative reduced cost, applies a labeling operation to it, and updates distance labels of vertices in v... |

57 |
Shortest path algorithms
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(Show Context)
Citation Context ...aph has a negative cycle, the distance labels maintained by the labeling method (with no cycle detection) will get arbitrarily negative. Most experimental studies of shortest path algorithms, such as =-=[2, 5, 8, 17]-=-, were conducted on graphs with no negative cycles. In this paper we study the practical performance of algorithms for the negative cycle problem. We also show that a cycle detection strategy of Tarja... |

56 | Scaling algorithms for the shortest paths problem
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(Show Context)
Citation Context ...enote the number of vertices and arcs in the network, respectively. With the additional assumption that arc lengths are integers bounded below by \GammaNs\Gamma2, the O( p nm log N) bound of Goldberg =-=[11]-=- improves the Bellman-- Ford--Moore bound unless N is very large. The same bounds hold for the negative cycle problem. All known algorithms for the negative cycle problem combine a shortest path algor... |

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Citation Context ...aph has a negative cycle, the distance labels maintained by the labeling method (with no cycle detection) will get arbitrarily negative. Most experimental studies of shortest path algorithms, such as =-=[2, 5, 8, 17]-=-, were conducted on graphs with no negative cycles. In this paper we study the practical performance of algorithms for the negative cycle problem. We also show that a cycle detection strategy of Tarja... |

34 |
Network Flow Theory
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(Show Context)
Citation Context ...egy. We study combinations of shortest path algorithms and cycle detection strategies to determine the best combination. The shortest path algorithms we study are based on the labeling method of Ford =-=[6, 7]-=-. Most cycle detection strategies for the labeling method look for cycles in the graph of parent pointers maintained by the method. The facts that these cycles correspond to negative cycles in the inp... |

24 | A primal method for minimal cost flows with applications to the assignment and transportation problems
- Klein
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(Show Context)
Citation Context ...e cycles. The negative cycle problem comes up both directly, for example in currency arbitrage, and as a subproblem in algorithms for other network problems, for example the minimum-cost flow problem =-=[14]-=-. The best theoretical time bound, O(nm), for the shortest path problem is achieved by the Bellman--Ford--Moore algorithm [1, 7, 18]. Here n and m denote the number of vertices and arcs in the network... |

21 |
Computational study of an improved shortest path algorithm, Networks 14
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(Show Context)
Citation Context ...fferent algorithms. In this section we discuss some of these strategies and algorithms. We do not discuss some of the algorithms such as the Pape--Levit algorithm [16, 20] and the threshold algorithm =-=[9, 10]-=-, which were not as robust as other algorithms in our previous study [2]. 5.1 The Bellman--Ford--Moore Algorithm The Bellman--Ford--Moore algorithm, due to Bellman [1], Ford [7], and Moore [18], maint... |

20 |
Implementation and Efficiency of Moore Algorithms for the Shortest Root Problem
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(Show Context)
Citation Context |

19 | A heuristic improvement of the Bellmanâ€“Ford algorithm
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(Show Context)
Citation Context ...ous codes and are a good choice for many practical situations. The previously known shortest path algorithms we study are the classical Bellman--Ford-- Moore algorithm; the Goldberg--Radzik algorithm =-=[12]-=-, which on shortest path problems per1 formed very well in a previous study [2]; an incremental graph algorithm of Pallottino [19], which performs well on some classes of shortest path problems; and a... |

18 |
A new polynomially bounded shortest path algorithm
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(Show Context)
Citation Context ...fferent algorithms. In this section we discuss some of these strategies and algorithms. We do not discuss some of the algorithms such as the Pape--Levit algorithm [16, 20] and the threshold algorithm =-=[9, 10]-=-, which were not as robust as other algorithms in our previous study [2]. 5.1 The Bellman--Ford--Moore Algorithm The Bellman--Ford--Moore algorithm, due to Bellman [1], Ford [7], and Moore [18], maint... |

13 |
Shortest path algorithms: A computational study with the C programming language
- Mondou, Crainic, et al.
- 1991
(Show Context)
Citation Context |

8 |
Shortest paths
- Tarjan
- 1981
(Show Context)
Citation Context ...were conducted on graphs with no negative cycles. In this paper we study the practical performance of algorithms for the negative cycle problem. We also show that a cycle detection strategy of Tarjan =-=[21]-=- leads to improved algorithms for the shortest path problem. These algorithms are usually competitive with the fastest previous codes and are a good choice for many practical situations. The previousl... |

5 |
Neleneinye Setevye Transportnye Zadachi. Transport
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(Show Context)
Citation Context |