Some Complexity Results for the k-Splittable Flow Minimizing Congestion Problem ()
ABSTRACT
In this paper, we mainly consider the complexity of the k-splittable flow minimizing congestion problem. We give some complexity results. For the k-splittable flow problem, the existence of a feasible solution is strongly NP-hard. When the number of the source nodes is an input, for the uniformly exactly k-splittable flow problem, obtaining an approximation algorithm with performance ratio better than (√5+1)/2 is NP-hard. When k is an input, for single commodity k-splittable flow problem, obtaining an algorithm with performance ratio better than is NP-hard. In the last of the paper, we study the relationship of minimizing congestion and minimizing number of rounds in the k-splittable flow problem. The smaller the congestion is, the smaller the number of rounds.
Share and Cite:
Jiao, C. , Feng, Q. and Bu, W. (2018) Some Complexity Results for the k-Splittable Flow Minimizing Congestion Problem.
Communications and Network,
10, 1-10. doi:
10.4236/cn.2018.101001.
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