Abstract Based on the dynamic quotient space model,the definitions of the max-flow and min-cut,and the condition that min-cut theorem holds in dynamic networks,are investigated. The analysis of the characteristics of max-flow in dynamic networks shows if the max-flow concept in the static environment is simply transferred to the dynamic one,the transformed max-flow does not have the two main properties,i.e. the additivity and total flow maximization. By introducing the concept of t-cut networks,a dynamic network is transformed into the combination of a set of static networks. Therefore,a new definition of the max-flow (steepest flow) is proposed and the defined concept is proved to have the above two properties. Then,a corresponding min-cut concept is presented and it is proved that the min-cut theorem holds under the new concepts of max-flow and min-cut. Finally,the algorithm for computing dynamic max-flow (steepest flow) is given.
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2013, Vol. 26 
