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Relations of the Set Cover Conjecture and Max-3-SAT Hypothesis to SETH

Determine whether the Set Cover Conjecture or the Max-3-SAT Hypothesis implies SETH or is implied by SETH.

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Background

Beyond SETH, 3SUM, and APSP, the paper reviews additional prominent hypotheses such as the Set Cover Conjecture (SCC) and the Max-3-SAT Hypothesis, both of which underpin numerous conditional lower bounds.

The precise implication relations between these hypotheses and SETH remain unsettled, and resolving them would significantly clarify the landscape of fine-grained assumptions.

References

It is an open problem whether either one of these hypothesis implies or is implied by the SETH.

— k-SUM Hardness Implies Treewidth-SETH (2510.08185 - Lampis, 9 Oct 2025) in Section: Other related work