# An approximation algorithm for minimizing congestion in the single-source k-splittable flow

### An approximation algorithm for minimizing congestion in the single-source k-splittable flow

Chengwen Jiao*, Qi Feng, Weichun Bu

College of Science, Zhongyuan University of Technology, Zhengzhou, Henan 450007, People’s Republic of China

In the traditional multi-commodity transmission networks, the number of paths each commodity can use is unrestricted, and the commodities can use arbitrary number of paths to transmit the flow. However, in the real transmission networks, too many paths will increase the total transmission cost of the network and also cause difficulties in the management of the network. In 2002, Baier[1] proposed the-splittable flow problem, in which each commodity can only use a limited number of paths to transmit the flow. In this paper, we study the-splittable multi-commodity transmission flow problem with the objective of minimizing congestion and cost. We propose an approximation algorithm with performance ratio  for congestion and cost in the single-source case, in which is the minimum value of the number of paths each commodity can use. The congestion reflects the total load of the network to some extent. The main aim of minimizing congestion is to distribute the demands of the commodities on the network in a balanced way, avoiding the case that some edge is used too much. By this way, the performance of the network as a whole can be guaranteed and more commodities can be served.

Keywords: k-splittable flow, congestion minimization, approximation algorithm

Chengwen Jiao et al., An approximation algorithm for minimizing congestion in the single-source k-splittable flow. Research Journal of Mathematics and Computer Science, 2017; 1:8. DOI:10.28933/rjmcs-2017-11-1405

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