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MINIMUM COST TOPOLOGICAL ORDERING

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journal contribution
posted on 2019-02-21, 08:32 authored by Thinh D. NguyenThinh D. Nguyen
We are given an $n$ vertex directed graph $G=(V,E)$ and also given a cost function $c:V\times [n]\to \mathbb{R}$. Consider a topological ordering of the vertices, $v_1,\ldots,v_n$, the cost of the ordering is $\sum_{i=1}^n c(v_i,i)$. We shall prove that finding the minimum cost topological ordering is $\mathrm{NP}$-hard.

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