An $$O(n(m+n\log n)\log n)$$O(n(m+nlogn)logn) time algorithm to solve the minimum cost tension problem

Abstract

This paper presents an $$O(n(m+n\log n)\log n)$$ time algorithm to solve the minimum cost tension problem, where n and m denote the number of nodes and number of arcs, respectively. The algorithm is inspired by Orlin (Oper Res 41:338–350, 1993) and improves upon the previous best strongly polynomial time of $$O(\max \{m^3n, m^2\log n(m+n\log n)\})$$ due to Ghiyasvand (J Comb Optim 34:203–217, 2017).