### Abstract

Let N = (V, A, c, l) be a network with node set V, arc set A, non-negative arc capacity function c and non-negative arc delay function l. We are interested in the fastest way to transmit f amount of data from a designated source node s ∈ V to a designated destination node d ∈ V. When the transmission is restricted to a single path, the problem is called the quickest path problem which has been well studied in the past few years and many efficient algorithms are known. When the transmission is not restricted to a single path, the problem is called the quickest flow problem or the minimum transmission time problem in the literature. Since data transmission is not restricted to a single path in the minimum transmission time problem, the problem was believed to be harder. In (Kagaris et al., 1995), it was proved that the minimum transmission time problem with integer capacities and real delays is NP-hard. In this paper, we show that the minimum transmission time problem with integer capacities and integer delays is equivalent to the maximal dynamic flow problem studied by Ford and Fulkerson in 1962 and therefore can be solved efficiently by their path decomposition algorithm.

Original language | English (US) |
---|---|

Pages (from-to) | 127-132 |

Number of pages | 6 |

Journal | Information Processing Letters |

Volume | 66 |

Issue number | 3 |

State | Published - May 15 1998 |

Externally published | Yes |

### Fingerprint

### Keywords

- Algorithms
- Communication networks
- Maximal dynamic flows
- Minimum transmission time
- Quickest paths
- Shortest paths

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Information Processing Letters*,

*66*(3), 127-132.

**Fast data transmission and maximal dynamic flow.** / Xue, Guoliang; Sun, Shangzhi; Rosen, J. Ben.

Research output: Contribution to journal › Article

*Information Processing Letters*, vol. 66, no. 3, pp. 127-132.

}

TY - JOUR

T1 - Fast data transmission and maximal dynamic flow

AU - Xue, Guoliang

AU - Sun, Shangzhi

AU - Rosen, J. Ben

PY - 1998/5/15

Y1 - 1998/5/15

N2 - Let N = (V, A, c, l) be a network with node set V, arc set A, non-negative arc capacity function c and non-negative arc delay function l. We are interested in the fastest way to transmit f amount of data from a designated source node s ∈ V to a designated destination node d ∈ V. When the transmission is restricted to a single path, the problem is called the quickest path problem which has been well studied in the past few years and many efficient algorithms are known. When the transmission is not restricted to a single path, the problem is called the quickest flow problem or the minimum transmission time problem in the literature. Since data transmission is not restricted to a single path in the minimum transmission time problem, the problem was believed to be harder. In (Kagaris et al., 1995), it was proved that the minimum transmission time problem with integer capacities and real delays is NP-hard. In this paper, we show that the minimum transmission time problem with integer capacities and integer delays is equivalent to the maximal dynamic flow problem studied by Ford and Fulkerson in 1962 and therefore can be solved efficiently by their path decomposition algorithm.

AB - Let N = (V, A, c, l) be a network with node set V, arc set A, non-negative arc capacity function c and non-negative arc delay function l. We are interested in the fastest way to transmit f amount of data from a designated source node s ∈ V to a designated destination node d ∈ V. When the transmission is restricted to a single path, the problem is called the quickest path problem which has been well studied in the past few years and many efficient algorithms are known. When the transmission is not restricted to a single path, the problem is called the quickest flow problem or the minimum transmission time problem in the literature. Since data transmission is not restricted to a single path in the minimum transmission time problem, the problem was believed to be harder. In (Kagaris et al., 1995), it was proved that the minimum transmission time problem with integer capacities and real delays is NP-hard. In this paper, we show that the minimum transmission time problem with integer capacities and integer delays is equivalent to the maximal dynamic flow problem studied by Ford and Fulkerson in 1962 and therefore can be solved efficiently by their path decomposition algorithm.

KW - Algorithms

KW - Communication networks

KW - Maximal dynamic flows

KW - Minimum transmission time

KW - Quickest paths

KW - Shortest paths

UR - http://www.scopus.com/inward/record.url?scp=0012360066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012360066&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012360066

VL - 66

SP - 127

EP - 132

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 3

ER -