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On a DAG Partitioning Problem

  • Soroush Alamdari
  • Abbas Mehrabian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7323)

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 ε > 0, there is no (n 1 − 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.

Keywords

DAG Partitioning Inapproximability Reduction 3-SAT pathwidth fixed parameter tractable 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Soroush Alamdari
    • 1
  • Abbas Mehrabian
    • 2
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooCanada

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