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Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems

Authors Matthias Bentert, Fedor V. Fomin , Tanmay Inamdar , Saket Saurabh

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Author Details

Matthias Bentert
  • University of Bergen, Norway
Fedor V. Fomin
  • University of Bergen, Norway
Tanmay Inamdar
  • Indian Institute of Technology Jodhpur, India
Saket Saurabh
  • The Institute of Mathematical Sciences, Chennai, India
  • University of Bergen, Norway

Funding

  • Bentert, Matthias: Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819416).
  • Fomin, Fedor V.: Supported by the Research Council of Norway via the project BWCA (grant no. 314528).
  • Inamdar, Tanmay: Supported by IITJ Research Initiation Grant (grant number I/RIG/TNI/ 20240072).
  • Saurabh, Saket: Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819416); and he also acknowledges the support of Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18.

Cite As Get BibTex

Matthias Bentert, Fedor V. Fomin, Tanmay Inamdar, and Saket Saurabh. Exponential-Time Approximation (Schemes) for Vertex-Ordering Problems. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.15

Abstract

In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest known (exponential-time) exact algorithms and the best known approximation factors that can be achieved in polynomial time? Following the recent research initiated by Esmer et al. (ESA 2022, IPEC 2023, SODA 2024) on vertex-subset problems, and by Inamdar et al. (ITCS 2024) on graph-partitioning problems, we focus on vertex-ordering problems. In particular, we give positive results for Feedback Arc Set, Optimal Linear Arrangement, Cutwidth, and Pathwidth. Most of our algorithms build upon a novel "balanced-cut" approach - which is our main conceptual contribution. This allows us to solve various problems in very general settings allowing for directed and arc-weighted input graphs. Our main technical contribution is a (1+ε)-approximation for any ε > 0 for (weighted) Feedback Arc Set in O^*((2-δ_ε)^n) time, where δ_ε > 0 is a constant only depending on ε.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Mathematics of computing → Graph algorithms
Keywords
  • Feedback Arc Set
  • Cutwidth
  • Optimal Linear Arrangement
  • Pathwidth

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