On the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures

  • Michael Lampis
  • Georgia Kaouri
  • Valia Mitsou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


We place our focus on the gap between treewidth’s success in producing fixed-parameter polynomial algorithms for hard graph problems, and specifically Hamiltonian Circuit and Max Cut, and the failure of its directed variants (directed tree-width [9], DAG-width [11] and kelly-width [8]) to replicate it in the realm of digraphs. We answer the question of why this gap exists by giving two hardness results: we show that Directed Hamiltonian Circuit is W[2]-hard when the parameter is the width of the input graph, for any of these widths, and that Max Di Cut remains NP-hard even when restricted to DAGs, which have the minimum possible width under all these definitions. Our results also apply to directed pathwidth.


Treewidth Digraph decompositions Parameterized Complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael Lampis
    • 1
  • Georgia Kaouri
    • 2
  • Valia Mitsou
    • 1
  1. 1.City University of New YorkUSA
  2. 2.National Technical University of AthensGreece

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