On a DAG partitioning problem

Authors:
Soroush Alamdari;Abbas Mehrabian
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Canada;Department of Combinatorics and Optimization, University of Waterloo, Canada
Venue:
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
Year:
2012

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Abstract

We study the following DAG Partitioning problem: given a directed acyclic graph with arc weights, delete a set of arcs of minimum total weight so that each of the resulting connected components has exactly one sink. We prove that the problem is hard to approximate in a strong sense: If $\mathcal P\neq \mathcal{NP}$ then for every fixed ε0, there is no (n1−ε)-approximation algorithm, even if the input graph is restricted to have unit weight arcs, maximum out-degree three, and two sinks. We also present a polynomial time algorithm for solving the DAG Partitioning problem in graphs with bounded pathwidth.