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Width Notions for Ordering-Related Problems

Authors Emmanuel Arrighi , Henning Fernau , Mateus de Oliveira Oliveira , Petra Wolf

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Author Details

Emmanuel Arrighi
  • University of Bergen, Norway
Henning Fernau
  • University of Trier, Germany
Mateus de Oliveira Oliveira
  • University of Bergen, Norway
Petra Wolf
  • University of Trier, Germany

Funding

  • Arrighi, Emmanuel: Research Council of Norway (Grant no. 274526), IS-DAAD (Grant no. 309319).
  • Fernau, Henning: DAAD PPP (Grant no. 57525246).
  • de Oliveira Oliveira, Mateus: Trond Mohn Foundation, Research Council of Norway (Grant no. 288761), IS-DAAD (Grant no. 309319).
  • Wolf, Petra: DFG project FE 560/9-1, DAAD PPP (Grant no. 57525246).

Cite As Get BibTex

Emmanuel Arrighi, Henning Fernau, Mateus de Oliveira Oliveira, and Petra Wolf. Width Notions for Ordering-Related Problems. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.FSTTCS.2020.9

Abstract

We are studying a weighted version of a linear extension problem, given some finite partial order ρ, called Completion of an Ordering. While this problem is NP-complete, we show that it lies in FPT when parameterized by the interval width of ρ. This ordering problem can be used to model several ordering problems stemming from diverse application areas, such as graph drawing, computational social choice, or computer memory management. Each application yields a special ρ. We also relate the interval width of ρ to parameterizations such as maximum range that have been introduced earlier in these applications, sometimes improving on parameterized algorithms that have been developed for these parameterizations before. This approach also gives some practical sub-exponential time algorithms for ordering problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Dynamic programming
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Parameterized algorithms
  • interval width
  • linear extension
  • one-sided crossing minimization
  • Kemeny rank aggregation
  • grouping by swapping

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