Advertisement

Parameterized Complexity of DAG Partitioning

  • René van Bevern
  • Robert Bredereck
  • Morgan Chopin
  • Sepp Hartung
  • Falk Hüffner
  • André Nichterlein
  • Ondřej Suchý
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7878)

Abstract

The goal of tracking the origin of short, distinctive phrases (memes) that propagate through the web in reaction to current events has been formalized as DAG Partitioning: given a directed acyclic graph, delete edges of minimum weight such that each resulting connected component of the underlying undirected graph contains only one sink. Motivated by NP-hardness and hardness of approximation results, we consider the parameterized complexity of this problem. We show that it can be solved in O(2 k ·n 2) time, where k is the number of edge deletions, proving fixed-parameter tractability for parameter k. We then show that unless the Exponential Time Hypothesis (ETH) fails, this cannot be improved to 2 o(k) ·n O(1); further, DAG Partitioning does not have a polynomial kernel unless NP ⊆ coNP/poly. Finally, given a tree decomposition of width w, we show how to solve DAG Partitioning in \(2^{O(w^2)}\cdot n\) time, improving a known algorithm for the parameter pathwidth.

Keywords

Directed Acyclic Graph Undirected Graph Input Graph Tree Decomposition Reduction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alamdari, S., Mehrabian, A.: On a DAG partitioning problem. In: Bonato, A., Janssen, J. (eds.) WAW 2012. LNCS, vol. 7323, pp. 17–28. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Cross-composition: A new technique for kernelization lower bounds. In: Proc. 28th STACS. LIPIcs, vol. 9, pp. 165–176. Dagstuhl Publishing (2011)Google Scholar
  3. 3.
    Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864–894 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
  5. 5.
    Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? J. Comput. System Sci. 63(4), 512–530 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Leskovec, J., Backstrom, L., Kleinberg, J.M.: Meme-tracking and the dynamics of the news cycle. In: Proc.15th ACM SIGKDD, pp. 497–506. ACM (2009)Google Scholar
  7. 7.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
  8. 8.
    Xiao, M.: Simple and improved parameterized algorithms for multiterminal cuts. Theory Comput. Syst. 46, 723–736 (2010)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • René van Bevern
    • 1
  • Robert Bredereck
    • 1
  • Morgan Chopin
    • 2
  • Sepp Hartung
    • 1
  • Falk Hüffner
    • 1
  • André Nichterlein
    • 1
  • Ondřej Suchý
    • 3
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.LAMSADEUniversité Paris-DauphineFrance
  3. 3.Faculty of Information TechnologyCzech Technical University in PraguePragueCzech Republic

Personalised recommendations