More consequences of falsifying SETH and the orthogonal vectors conjecture

Amir Abboud, Holger Dell, Karl Bringmann, Jesper Nederlof

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

7 Citaten (Scopus)

Samenvatting

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).

Originele taal-2Engels
TitelSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
Plaats van productieNew York
UitgeverijAssociation for Computing Machinery, Inc
Pagina's253-266
Aantal pagina's12
ISBN van elektronische versie978-1-4503-5559-9
DOI's
StatusGepubliceerd - 20 jun 2018
Evenement50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, Verenigde Staten van Amerika
Duur: 25 jun 201829 jun 2018

Congres

Congres50th Annual ACM Symposium on Theory of Computing, STOC 2018
LandVerenigde Staten van Amerika
StadLos Angeles
Periode25/06/1829/06/18

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  • Citeer dit

    Abboud, A., Dell, H., Bringmann, K., & Nederlof, J. (2018). More consequences of falsifying SETH and the orthogonal vectors conjecture. In STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (blz. 253-266). Association for Computing Machinery, Inc. https://doi.org/10.1145/3188745.3188938