License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.41
URN: urn:nbn:de:0030-drops-74419
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7441/
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Alman, Josh ; Mnich, Matthias ; Vassilevska Williams, Virginia

Dynamic Parameterized Problems and Algorithms

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LIPIcs-ICALP-2017-41.pdf (0.6 MB)

Abstract

Fixed-parameter algorithms and kernelization are two powerful methods to solve NP-hard problems. Yet, so far those algorithms have been largely restricted to static inputs. In this paper we provide fixed-parameter algorithms and kernelizations for fundamental NP-hard problems with dynamic inputs. We consider a variety of parameterized graph and hitting set problems which are known to have f(k)n^{1+o(1)} time algorithms on inputs of size n, and we consider the question of whether there is a data structure that supports small updates (such as edge/vertex/set/element insertions and deletions) with an update time of g(k)n^{o(1)}; such an update time would be essentially optimal. Update and query times independent of n are particularly desirable. Among many other results, we show that Feedback Vertex Set and k-Path admit dynamic algorithms with f(k)log O(1) n update and query times for some function f depending on the solution size k only.

We complement our positive results by several conditional and unconditional lower bounds. For example, we show that unlike their undirected counterparts, Directed Feedback Vertex Set and Directed k-Path do not admit dynamic algorithms with n^{o(1) } update and query times even for constant solution sizes k <= 3, assuming popular hardness hypotheses. We also show that unconditionally, in the cell probe model, Directed Feedback Vertex Set cannot be solved with update time that is purely a function of k.

BibTeX - Entry

@InProceedings{alman_et_al:LIPIcs:2017:7441,
  author =	{Josh Alman and Matthias Mnich and Virginia Vassilevska Williams},
  title =	{{Dynamic Parameterized Problems and Algorithms}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7441},
  URN =		{urn:nbn:de:0030-drops-74419},
  doi =		{10.4230/LIPIcs.ICALP.2017.41},
  annote =	{Keywords: Dynamic algorithms, fixed-parameter algorithms}
}

Keywords: Dynamic algorithms, fixed-parameter algorithms
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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