A Strongly Polynomial Algorithm for Minimum Cost Submodular Flow Problems

1989 ◽  
Vol 14 (1) ◽  
pp. 60-69 ◽  
Author(s):  
Satoru Fujishige ◽  
Hans Röck ◽  
Uwe Zimmermann
2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jianping Li ◽  
Juanping Zhu

This paper considers the general capacity expansion path problem (GCEP) for the telecommunication operators. We investigate the polynomial equivalence between the GCEP problem and the constrained shortest path problem (CSP) and present a pseudopolynomial algorithm for the GCEP problem, no matter the graph is acyclic or not. Furthermore, we investigate two special versions of the GCEP problem. For the minimum number arc capacity expansion path problem (MN-CEP), we give a strongly polynomial algorithm based on the dynamic programming. For the minimum-cost capacity expansion shortest path problem (MCESP), we give a strongly polynomial algorithm by constructing a shortest paths network.


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