More consequences of falsifying SETH and the orthogonal vectors conjecture

Amir Abboud, Holger Dell, Karl Bringmann, Jesper Nederlof

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

15 Citations (Scopus)

Abstract

The Strong Exponential Time Hypothesis and the OV-conjecture are two popular hardness assumptions used to prove a plethora of lower bounds, especially in the realm of polynomial-time algorithms. The OV-conjecture in moderate dimension States there is no > 0 for which an O(N2−ε) poly(D) time algorithm can decide whether there is a pair of orthogonal vectors in a given set of size N that contains D-dimensional binary vectors. We strengthen the evidence for these hardness assumptions. In particular, we show that if the OV-conjecture fails, then two problems for which we are far from obtaining even tiny improvements over exhaustive search would have surprisingly fast algorithms. If the OV conjecture is false, then there is a fixed > 0 such that: (1) For all d and all large enough k, there is a randomized algorithm that takes O(n(1−ε)k) time to solve the Zero-Weight-k-Clique and Min-Weight-k-Clique problems on d-hypergraphs with n vertices. As a consequence, the OV-conjecture is implied by the Weighted Clique conjecture. (2) For all c, the satisfiability of sparse TC1 circuits on n inputs (that is, circuits with cn wires, depth c log n, and negation, AND, OR, and threshold gates) can be computed in time O((2 −)n).

Original languageEnglish
Title of host publicationSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
EditorsMonika Henzinger, David Kempe, Ilias Diakonikolas
Place of PublicationNew York
PublisherAssociation for Computing Machinery, Inc
Pages253-266
Number of pages14
ISBN (Electronic)978-1-4503-5559-9
DOIs
Publication statusPublished - 20 Jun 2018
Event50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States
Duration: 25 Jun 201829 Jun 2018

Conference

Conference50th Annual ACM Symposium on Theory of Computing, STOC 2018
Country/TerritoryUnited States
CityLos Angeles
Period25/06/1829/06/18

Keywords

  • Clique
  • Fine-grained complexity
  • OV
  • Satisfiability
  • Threshold circuits
  • fine-grained complexity
  • clique
  • satisfiability
  • threshold circuits

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