Document Open Access Logo

Turbocharging Treewidth Heuristics

Authors Serge Gaspers, Joachim Gudmundsson, Mitchell Jones, Julián Mestre, Stefan Rümmele

PDF

File

Thumbnail PDF
PDF
LIPIcs.IPEC.2016.13.pdf
  • Filesize: 0.59 MB
  • 13 pages

Document Identifiers

Subject Classification

Keywords
  • tree decomposition
  • heuristic
  • fixed-parameter tractability
  • local search

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

A widely used class of algorithms for computing tree decompositions of graphs are heuristics that compute an elimination order, i.e., a permutation of the vertex set. In this paper, we propose to turbocharge these heuristics. For a target treewidth k, suppose the heuristic has already computed a partial elimination order of width at most k, but extending it by one more vertex exceeds the target width k. At this moment of regret, we solve a subproblem which is to recompute the last c positions of the partial elimination order such that it can be extended without exceeding width k. We show that this subproblem is fixed-parameter tractable when parameterized by k and c, but it is para-NP-hard and W[1]-hard when parameterized by only k or c, respectively. Our experimental evaluation of the FPT algorithm shows that we can trade a reasonable increase of the running time for quality of the solution.

Cite As Get BibTex

Serge Gaspers, Joachim Gudmundsson, Mitchell Jones, Julián Mestre, and Stefan Rümmele. Turbocharging Treewidth Heuristics. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.IPEC.2016.13

Author Details

Serge Gaspers
Joachim Gudmundsson
Mitchell Jones
Julián Mestre
Stefan Rümmele

References

  1. Stefan Arnborg, Derek G. Corneil, and Andrzej Proskurowski. Complexity of finding embeddings in ak-tree. SIAM Journal on Algebraic Discrete Methods, 8(2):277-284, 1987. Google Scholar
  2. Hans L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996. Google Scholar
  3. Hans L. Bodlaender and Arie M. C. A. Koster. Treewidth computations I. Upper bounds. Inf. Comput., 208(3):259-275, 2010. URL: http://dx.doi.org/10.1016/j.ic.2009.03.008.
  4. Rodney G. Downey and Michael R. Fellows. Fixed-parameter tractability and completeness II: on completeness for W[1]. Theor. Comput. Sci., 141(1&2):109-131, 1995. Google Scholar
  5. Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. Google Scholar
  6. Vibhav Gogate and Rina Dechter. A complete anytime algorithm for treewidth. In Proc. of UAI'04, pages 201-208. AUAI Press, 2004. Google Scholar
  7. Sepp Hartung and Rolf Niedermeier. Incremental list coloring of graphs, parameterized by conservation. Theor. Comput. Sci., 494:86-98, 2013. Google Scholar
  8. Arie M. C. A. Koster, Hans L. Bodlaender, and Stan P. M. van Hoesel. Treewidth: Computational experiments. Electronic Notes in Discrete Mathematics, 8:54-57, 2001. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact