Parameterized Aspects of Triangle Enumeration

  • Matthias Bentert
  • Till Fluschnik
  • André Nichterlein
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10472)

Abstract

Listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to both theoretical aspects (e.g., lower and upper bounds on running time, adaption to new computational models) as well as practical aspects (e.g. algorithms tuned for large graphs). Motivated by the fact that the worst-case running time is cubic, we perform a systematic parameterized complexity study of triangle enumeration, providing both positive results (new enumerative kernelizations, “subcubic” parameterized solving algorithms) as well as negative results (uselessness in terms of possibility of “faster” parameterized algorithms of certain parameters such as diameter).

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Matthias Bentert
    • 1
  • Till Fluschnik
    • 1
  • André Nichterlein
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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