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A linear-time parameterized algorithm for computing the width of a DAG
[article]
2021
arXiv
pre-print
The width k of a directed acyclic graph (DAG) G = (V, E) equals the largest number of pairwise non-reachable vertices. Computing the width dates back to Dilworth's and Fulkerson's results in the 1950s, and is doable in quadratic time in the worst case. Since k can be small in practical applications, research has also studied algorithms whose complexity is parameterized on k. Despite these efforts, it is still open whether there exists a linear-time O(f(k)(|V| + |E|)) parameterized algorithm
arXiv:2007.07575v3
fatcat:a2heul76azawbhoz26jwcbl44a