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Threshold Rounding and Bounded-Degree Boolean MAX 2-CSP

Authors Suprovat Ghoshal , Neng Huang , Euiwoong Lee , Konstantin Makarychev , Yury Makarychev

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ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • MAX 2-SAT
  • Approximation Algorithms
  • Constraint Satisfaction Problems

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Abstract

We describe an Ω̃(1/d⁴)-improvement over threshold rounding schemes for a broad class of Boolean MAX 2-CSP instances in which every variable appears in at most d constraints. In the case of MAX 2-SAT, we improve the ratio further and obtain an (β_⋆ + Ω̃(1/d²))-factor approximation algorithm for bounded-degree MAX 2-SAT instances, where β_⋆ is the UGC-optimal approximation ratio for MAX 2-SAT achieved by the LLZ algorithm [Lewin et al., 2002]. Our result generalizes an (α_GW + Ω̃(1/d²))-factor approximation algorithm for MAX CUT on graphs with degrees bounded by d, due to Hsieh and Kothari [Hsieh and Kothari, 2023]. Together with the state-of-the-art approximability results for MAX DI-CUT and MAX 2-AND [Brakensiek et al., 2023], our result suggests that similar improvements exist for bounded-degree instances of these problems as well.

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Suprovat Ghoshal, Neng Huang, Euiwoong Lee, Konstantin Makarychev, and Yury Makarychev. Threshold Rounding and Bounded-Degree Boolean MAX 2-CSP. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.28

Author Details

Suprovat Ghoshal
  • Indiana University, Bloomington, IN, USA
Neng Huang
  • University of Michigan, Ann Arbor, MI, USA
Euiwoong Lee
  • University of Michigan, Ann Arbor, MI, USA
Konstantin Makarychev
  • Northwestern University, Evanston, IL, USA
Yury Makarychev
  • Toyota Technological Institute at Chicago, IL, USA

Funding

  • Lee, Euiwoong: Supported in part by NSF award CCF-2236669.
  • Makarychev, Konstantin: Supported by NSF awards CCF-1955351 and EECS-2216970.
  • Makarychev, Yury: Supported by NSF award EECS-2216899

References

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