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## Discrete dynamic shortest path problems in transportation applications: Complexity and algorithms with optimal run time (1999)

Venue: | 234 I. Chabini. Minimum expected travel times in stochastic time-dependent networks revisited. Internal Report. MIT |

Citations: | 78 - 2 self |

### Citations

1087 |
A note on two problems in connection with graphs." Numerische Mathematik(1
- Dijkstra
- 1959
(Show Context)
Citation Context ...s Is Not Allowed This is the most studied variation of the problem (4,5,7). The most celebrated result for this variation of the problem is the following: When the FIFO condition is valid, Dijkstra’s =-=(8)-=- algorithm can be generalized to solve the time-dependent fastest paths problem with the same time complexity as the static shortest paths problem. Dreyfus (7) was the first to mention this generaliza... |

213 | A Note on Two - Dijkstra - 1959 |

180 |
An Appraisal of Some Shortest-Path Algorithms.
- Dreyfus
- 1969
(Show Context)
Citation Context ...odes. We analyse the problem for the two types of waiting-at-node policies defined above. 3.1 Waiting at nodes is not allowed This is the most studied variation of the problem (Cook and Halsey, 1966; =-=Dreyfus, 1969-=-; Kaufman and Smith, 1993). The most celebrated result for this variation of the problem is the following: when the FIFO condition is valid, Dijkstra's algorithm can be generalized to solve the time-d... |

85 |
The shortest Route through a Network with Time-Dependent Internodal Transit Times.
- Cooke, Halsey
- 1966
(Show Context)
Citation Context ...tical findings. It is the first time that a solution algorithm with an optimal computation time complexity is proposed for what appears to be a 30-year-old problem first addressed by Cooke and Halsey =-=(4)-=-. DEFINITIONS AND NOTATION Let G = (N, A, D, C) be a directed network where N = {1, . . ., n} is the set of nodes and A = {(i,j) ∈ NxN} is the set of arcs (or links). The number of links (arcs) is den... |

80 |
Shortest Path Algorithms
- Gallo, Pallottino
- 1988
(Show Context)
Citation Context ...abel-correcting algorithms using three types of data structures for node candidates list: the Deque data structure (10) as described in Ziliaskopoulos and Mahmassani (6), the two-queue data structure =-=(11)-=-, and a three-queue data structure that extends the notion of the two-queue data structure (12). All algorithms were coded in C++. Algorithm DOT has very attractive properties. First, its computer cod... |

75 |
Shortest Path Algorithms: Taxonomy and annotation.
- Deo, Pang
- 1984
(Show Context)
Citation Context ...Dynamic Networks. 1. INTRODUCTION The shortest paths problem in networks has been the subject of extensive research for many years resulting in the publication of a large number of scientific papers (=-=Deo and Pang, 1984-=-). The analysis of transportation networks is one of the many application areas where the computation of shortest paths is one of the most fundamental problems.The vast majority of published research ... |

74 |
Fastest paths in time-dependent networks for intelligent vehicle-highway systems application.
- Kaufman, Smith
- 1993
(Show Context)
Citation Context ...dynamic network. Arc travel times may possess some properties useful in studying and developing algorithms for dynamic networks. A well celebrated property is the First-InFirst -Out (FIFO) condition (=-=Kaufman and Smith, 1993-=-) which may be defined in various mathematical forms. For instance, the FIFO condition is valid if and only if the following system of inequalities holds: When the FIFO condition holds, we say that th... |

37 |
Time-dependent, shortestpath algorithm for real-time intelligent vehicle highway system applications. Transportation research record, 1408, 94-100. Sadeghi-Niaraki, A .
- Ziliaskopoulos
- 1993
(Show Context)
Citation Context ...ontext of dynamic management of transportation systems. Most published work has dealt with the first question, with the exception of the work by Cooke and Halsey (4) and Ziliaskopoulos and Mahmassani =-=(6)-=-. Although algorithms that answer the first question can be used to answer the second question as well, such approaches would not be efficient for transportation networks because only a reduced subset... |

27 |
Implementation and Efficiency of Moore-Algorithms for the Shortest Route
- Pape
- 1974
(Show Context)
Citation Context ...all-to-one fastest paths problem are algorithm DOT and three dynamic adaptations of label-correcting algorithms using three types of data structures for node candidates list: the Deque data structure =-=(10)-=- as described in Ziliaskopoulos and Mahmassani (6), the two-queue data structure (11), and a three-queue data structure that extends the notion of the two-queue data structure (12). All algorithms wer... |

9 |
A flow-based approach to the dynamic traffic assignment problem: formulations, algorithms, and Computer Implementations. Msc Thesis
- He
- 1997
(Show Context)
Citation Context ... times of the length of discretization intervals. The travel times used were obtained from the output results of an analytical dynamic traffic assignment model developed by Chabini and He (13) and He =-=(14)-=-. Table 5 summarizes the results of this experience. Table 5 shows that run time of algorithm DOT is proportional to the number of time intervals or, equivTABLE 4 Computation Times for 10,000 Links, 6... |

5 |
Vehicle routing with time windows and time-varying
- Ahn, Shin
- 1991
(Show Context)
Citation Context ...problem. Dreyfus (7) was the first to mention this generalization. Later, Kaufman and Smith (5) formally proved that this generalization is valid only if the FIFO condition is satisfied. Ahn and Shin =-=(9)-=- provided an even earlier proof. A proof that is more insightful and simpler follows. The proof is based on a different formulation of the problem. Let f j denote the minimum travel time from origin n... |

3 |
A New Short Paths Algorithm for Discrete Dynamic Networks
- Chabini
- 1997
(Show Context)
Citation Context ..., 1974) as described in Ziliaskopoulos and Mahmassani (1993), the 2-queue data structure (Gallo and Pallotino,1988) and a 3-queue data structure that extends the notion of the 2-queue data structure (=-=Chabini, 1997-=-b). All algorithms were coded in C++. Codes are available upon request. Algorithm DOT has very attractive properties. First, its computer coding is a very easy task (if one has a static shortest paths... |

2 |
Fastest paths in dynamic networks
- Chabini
- 2000
(Show Context)
Citation Context ..., 1974) as described in Ziliaskopoulos and Mahmassani (1993), the 2-queue data structure (Gallo and Pallotino,1988) and a 3-queue data structure that extends the notion of the 2-queue data structure (=-=Chabini, 1997-=-b). All algorithms were coded in C++. Codes are available upon request. Algorithm DOT has very attractive properties. First, its computer coding is a very easy task (if one has a static shortest paths... |

2 |
An Analytical Approach to Dynamic Traffic Assignment: Models, Algorithms and Computer Implementations. Internal Report
- Chabini, He
- 1999
(Show Context)
Citation Context ...fects on run times of the length of discretization intervals. The travel times used were obtained from the output results of an analytical dynamic traffic assignment model developed by Chabini and He =-=(13)-=- and He (14). Table 5 summarizes the results of this experience. Table 5 shows that run time of algorithm DOT is proportional to the number of time intervals or, equivTABLE 4 Computation Times for 10,... |

1 | High Performance Computation of Temporal Shortest Routes for Intelligent Transportation Systems Applications - Chabini, Florian - 1995 |

1 | Distributed Computation of Shortest Paths and Network Equilibrium Models" appeared in the proceeding - Parallel |

1 |
Minimum Wait Paths in Time-Dependent Networks
- Orda, Rom
- 1991
(Show Context)
Citation Context ...dynamic shortest paths problems can be further subdivided into two types: discrete and continuous. In discrete dynamic networks, time is modelled as a set of integers. In continuous dynamic networks (=-=Orda and Rom, 1991-=-), time is treated as real numbers. It is important to mention that a discrete dynamic network can alternatively be viewed as a static network obtained by using a time-space expansion representation. ... |

1 |
Fastest Paths in Dynamic Networks. Transportation Science
- Chabini
(Show Context)
Citation Context ...eque data structure (10) as described in Ziliaskopoulos and Mahmassani (6), the two-queue data structure (11), and a three-queue data structure that extends the notion of the two-queue data structure =-=(12)-=-. All algorithms were coded in C++. Algorithm DOT has very attractive properties. First, its computer coding is a very easy task. Second, algorithm DOT does not need complicated data structures; a bas... |