Topological orderings of weighted directed acyclic graphs
Abstract
We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological orderings of weighted directed acyclic graphs. The first process is called a mark sequence and the second is a generalization called a mark-unmark sequence. We answer a question of Erickson by showing that every non-negative topological ordering that can be realized by a mark-unmark sequence can also be realized by a mark sequence. We also investigate the question of whether a given weighted directed acyclic graph has a non-negative topological ordering. We show that even in the simple case when every vertex is a source or a sink the question is NP-complete.
Cite
@article{arxiv.1310.0516,
title = {Topological orderings of weighted directed acyclic graphs},
author = {Dániel Gerbner and Balázs Keszegh and Cory Palmer and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1310.0516},
year = {2016}
}
Comments
Included an addendum remarking on an independent proof of one of our main theorems; added references; corrected typos