TY - JOUR

T1 - Fast data transmission and maximal dynamic flow

AU - Xue, Guoliang

AU - Sun, Shangzhi

AU - Rosen, J. Ben

N1 - Funding Information:
* Corresponding author. Email: xue@cs.uvm.edu. The research of this author was supported in part by the US Army Research Office grant DAAHO4-96-l-0233 and by the National Science Foundation grants ASC-9409285 and OSR-9350540. ’ Email: ssun@synopsys.com. * Email: rosen@cs.umn.edu.

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

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U2 - 10.1016/s0020-0190(98)00047-7

DO - 10.1016/s0020-0190(98)00047-7

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 -