Computing kernels in parallel: Lower and upper bounds

Max Bannach, Till Tantau


Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also efficiently compute small problem kernels in parallel: known kernelization algorithms are typically highly sequential. In the present paper, we establish a number of upper and lower bounds concerning the sizes of kernels that can be computed in parallel. An intriguing finding is that there are complex trade-offs between kernel size and the depth of the circuits needed to compute them: For the vertex cover problem, an exponential kernel can be computed by AC0-circuits, a quadratic kernel by TC0-circuits, and a linear kernel by randomized NC-circuits with derandomization being possible only if it is also possible for the matching problem. Other natural problems for which similar (but quantitatively different) effects can be observed include tree decomposition problems parameterized by the vertex cover number, the undirected feedback vertex set problem, the matching problem, or the point line cover problem. We also present natural problems for which computing kernels is inherently sequential.

Original languageEnglish
Title of host publication13th International Symposium on Parameterized and Exact Computation (IPEC 2018)
EditorsChristophe Paul, Michal Pilipczuk
Number of pages14
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication date01.01.2019
Article number13
ISBN (Print)978-3-95977-084-2
Publication statusPublished - 01.01.2019
Event13th International Symposium on Parameterized and Exact Computation - Helsinki, Finland
Duration: 22.08.201824.08.2018
Conference number: 163357

DFG Research Classification Scheme

  • 409-01 Theoretical Computer Science


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