## Shortest Paths Algorithms: Theory And Experimental Evaluation (1993)

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Venue: | Mathematical Programming |

Citations: | 146 - 14 self |

### BibTeX

@ARTICLE{Cherkassky93shortestpaths,

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

title = {Shortest Paths Algorithms: Theory And Experimental Evaluation},

journal = {Mathematical Programming},

year = {1993},

volume = {73},

pages = {129--174}

}

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### Abstract

. We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on several natural problem classes which identify strengths and weaknesses of various algorithms. These problem classes and algorithm implementations form an environment for testing the performance of shortest paths algorithms. The interaction between the experimental evaluation of algorithm behavior and the theoretical analysis of algorithm performance plays an important role in our research. Andrew V. Goldberg was supported in part by ONR Young Investigator Award N00014-91-J-1855, NSF Presidential Young Investigator Grant CCR-8858097 with matching funds from AT&T, DEC, and 3M, and a grant from Powell Foundation. This work was done while Boris V. Cherkassky was visiting Stanford University Compu...

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Citation Context ... of the v to s path in the tree is a shortest path from s to v. 3. The Labeling Method In this section we briefly outline the general labeling method for solving the shortest paths problem. (See e.g. =-=[4, 10, 23] for-=- more detail.) Most shortest paths algorithms are based on this method. For every node v, the method maintains its potential d(v), parent ��(v), and status S(v) 2 funreached; labeled; scannedg. Th... |

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Citation Context ... of the v to s path in the tree is a shortest path from s to v. 3. The Labeling Method In this section we briefly outline the general labeling method for solving the shortest paths problem. (See e.g. =-=[4, 10, 23] for-=- more detail.) Most shortest paths algorithms are based on this method. For every node v, the method maintains its potential d(v), parent ��(v), and status S(v) 2 funreached; labeled; scannedg. Th... |

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Citation Context ...or acyclic graphs, acc. Experiments with acyclic graphs are interesting for several reasons. Shortest paths problems in acyclic graphs come up in applications, such as PERT network analysis (see e.g. =-=[17]-=-). Furthermore, some networks that come up in applications have large acyclic subgraphs (e.g. electric networks) and an algorithm that behaves poorly on acyclic networks is likely to behave poorly on ... |

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Citation Context ...gorithms. Algorithms for this problem have been studied for a long time. See e.g. [2, 5, 6, 7, 18, 19, 21]. However, advances in the theory of shortest paths algorithms are still being made. See e.g. =-=[1, 9, 13]-=-. A good description of the classical algorithms and their implementations appears in [10]. On a network with negative-length arcs, the best currently known time bound of O(nm) is achieved by the Bell... |

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Citation Context ...8, 19, 21]. However, advances in the theory of shortest paths algorithms are still being made. See e.g. [1, 9, 13]. A good description of the classical algorithms and their implementations appears in =-=[10]-=-. On a network with negative-length arcs, the best currently known time bound of O(nm) is achieved by the Bellman-Ford-Moore algorithm [2, 7, 19]. (Here n and m denote the number of nodes and arcs in ... |

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Citation Context ...gorithms. Algorithms for this problem have been studied for a long time. See e.g. [2, 5, 6, 7, 18, 19, 21]. However, advances in the theory of shortest paths algorithms are still being made. See e.g. =-=[1, 9, 13]-=-. A good description of the classical algorithms and their implementations appears in [10]. On a network with negative-length arcs, the best currently known time bound of O(nm) is achieved by the Bell... |

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Citation Context ...t especially good, but a better implementation may be possible. A careful experimental study of several other methods, such as variations of the threshold algorithm [12, 10] and the auction algorithm =-=[3]-=-, may produce interesting results as well. We experimented with networks without negative cycles. An interesting question is which algorithms are best at detecting a negative cycle if there is one. Co... |

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Citation Context ...ementation Challenge [15]. In this paper we study practical performance of several shortest paths algorithms, including established methods [2, 6, 7, 11, 18, 19, 20, 21], recently proposed algorithms =-=[1, 14]-=-, and new algorithms. The development of the new algorithms was based on the experimental feedback. We give theoretical explanation of the observed behavior of the algorithms and prove complexity boun... |

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Citation Context .... 4.4. The Threshold Algorithm. Glover et. al. [11] suggest the following method, which combines the ideas lying behind the Bellman-Ford-Moore, Dijkstra's, and incremental graph algorithms. (See also =-=[12, 10]-=-.) The method partitions the set of labeled nodes into two subsets, NOW and NEXT, which are maintained as FIFO queues. At the beginning of each iteration of the algorithm, NOW is empty. The method als... |

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Citation Context ...anned previously and added to the tail of the queue otherwise. The algorithm terminates when both the stack and the queue are empty. This algorithm has exponential worst-case time bound. Theorem 4.8. =-=[16, 22]-=- The Pape-Levit algorithm runs in \Theta(n2 n ) time in the worst case. Pallottino's algorithm maintains S 1 and S 2 using FIFO queues, Q 1 and Q 2 . The next node to be scanned is removed from the he... |

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Citation Context ...ough the codes differ by only two statements. As we shall see later, bf performs much worse than some other codes on this problem. Note that stack has an exponential worst-case running time (see e.g. =-=[22]-=-). 4.1. Bellman-Ford-Moore Algorithm. The Bellman-Ford-Moore algorithm, due to Bellman [2], Ford [7], and Moore [19], maintains the set of labeled nodes in a FIFO queue. The next node to be scanned is... |