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Syntactic Separation of Subset Satisfiability Problems

Authors Eric Allender, Martín Farach-Colton, Meng-Tsung Tsai

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Author Details

Eric Allender
  • Rutgers University, Piscataway, NJ 08854, USA
Martín Farach-Colton
  • Rutgers University, Piscataway, NJ 08854, USA
Meng-Tsung Tsai
  • National Chiao Tung University, Hsinchu, Taiwan

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Eric Allender, Martín Farach-Colton, and Meng-Tsung Tsai. Syntactic Separation of Subset Satisfiability Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 16:1-16:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


Variants of the Exponential Time Hypothesis (ETH) have been used to derive lower bounds on the time complexity for certain problems, so that the hardness results match long-standing algorithmic results. In this paper, we consider a syntactically defined class of problems, and give conditions for when problems in this class require strongly exponential time to approximate to within a factor of (1-epsilon) for some constant epsilon > 0, assuming the Gap Exponential Time Hypothesis (Gap-ETH), versus when they admit a PTAS. Our class includes a rich set of problems from additive combinatorics, computational geometry, and graph theory. Our hardness results also match the best known algorithmic results for these problems.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Syntactic Class
  • Exponential Time Hypothesis
  • APX
  • PTAS


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