Efficient algorithms for measuring the funnel-likeness of DAGs
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We propose funnels as a new natural subclass of DAGs. Intuitively, a DAG is a funnel if every source-sink path can be uniquely identified by one of its arcs. Funnels are an analogue to trees for directed graphs, being more restrictive than DAGs but more expressive than mere in-/out-trees. Computational problems such as finding vertex-disjoint paths or tracking the origin of memes remain NP-hard on DAGs while on funnels they become solvable in polynomial time. Our main focus is the algorithmic complexity of finding out how funnel-like a given DAG is. To this end, we identify the NP-hard problem of computing the arc-deletion distance of a given DAG to a funnel. We develop efficient exact and approximation algorithms for the problem and test them on synthetic random graphs and real-world graphs.
KeywordsDirected graphs Acyclic digraph NP-hard problems Approximation hardness Fixed-parameter tractability Approximation algorithms Graph parameters Experiments
We are grateful to anonymous reviewers of Journal of Combinatorial Optimization whose constructive feedback helped to improve the presentation and remove some bugs from this paper.
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