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More consequences of falsifying SETH and the orthogonal vectors conjecture

Amir Abboud, Karl Bringmann, Holger Dell, Jesper Nederlof
2018 Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018  
The OV-conjecture in moderate dimension states there is no ϵ>0 for which an O(N^2-ϵ)poly(D) time algorithm can decide whether there is a pair of orthogonal vectors in a given set of size N that contains  ...  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 n, and negation  ...  We thank Ivan Mikhailin for a helpful comment on an earlier version of this manuscript.  ... 
doi:10.1145/3188745.3188938 dblp:conf/stoc/AbboudBDN18 fatcat:ab33jq6u3rdvxkz5pu3aqxsei4

Average-case fine-grained hardness

Marshall Ball, Alon Rosen, Manuel Sabin, Prashant Nalini Vasudevan
2017 Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017  
We also show how our reductions make conjectures regarding the worst-case hardness of the problems we reduce from (and consequently the Strong Exponential Time Hypothesis) heuristically falsifiable in  ...  We prove our hardness results in each case by showing fine-grained reductions from solving one of three problems -namely, Orthogonal Vectors (OV), 3SUM, and All-Pairs Shortest Paths (APSP) -in the worst  ...  Acknowledgements We would like to thank Amir Abboud for suggesting a barrier to achieving low-degree polynomials for EDIT-DISTANCE (Section 2.2) and for pointing us to the Triangle-Collection problem in  ... 
doi:10.1145/3055399.3055466 dblp:conf/stoc/BallRSV17 fatcat:a7xcqudairelvngogbqi245ltu

Parameterized Fine-Grained Reductions [article]

Elli Anastasiadi, Antonis Antonopoulos, Aris Pagourtzis, Stavros Petsalakis
2019 arXiv   pre-print
As an application of this framework we present a truly sub-quadratic fixed-parameter algorithm for the orthogonal vectors problem.  ...  During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community.  ...  Amir Abboud, Karl Bringmann, Holger Dell, and Jesper Nederlof. More consequences of falsifying SETH and the orthogonal vectors conjecture.  ... 
arXiv:1902.05529v1 fatcat:b2migtkxfvgajevtpkja7az75q

Distributed PCP Theorems for Hardness of Approximation in P [article]

Amir Abboud, Aviad Rubinstein, Ryan Williams
2017 arXiv   pre-print
In particular, for the first two problems we obtain nearly-polynomial factors of 2^( n)^1-o(1); only (1+o(1))-factor lower bounds (under SETH) were known before.  ...  ,x_n, and both parties know φ. The goal is to have Alice and Bob jointly write a PCP that x satisfies φ, while exchanging little or no information.  ...  This work was done in part at the Simons Institute for the Theory of Computing. We are also grateful to the organizers of Dagstuhl Seminar 16451 for a special collaboration opportunity.  ... 
arXiv:1706.06407v2 fatcat:xzapmrglobah5bgxdw7igrpvz4

Computing top-k Closeness Centrality Faster in Unweighted Graphs

Elisabetta Bergamini, Michele Borassi, Pierluigi Crescenzi, Andrea Marino, Henning Meyerhenke
2019 ACM Transactions on Knowledge Discovery from Data  
problem in O(|C| 2− ) would falsify the Orthogonal Vector conjecture.  ...  Moreover, it is well known that the Orthogonal Vector conjecture is implied by SETH [32, 10, 3] : consequently, the following corollary holds.  ... 
doi:10.1145/3344719 fatcat:hfuu46acanb2bl7gqtxoklkuhi

Fine-Grained Complexity and Conditional Hardness for Sparse Graphs [article]

Udit Agarwal, Vijaya Ramachandran
2017 arXiv   pre-print
We also identify Eccentricities as a key problem in the Õ(mn) class which is simultaneously MWCC-hard, SETH-hard and k-DSH-hard, where SETH is the Strong Exponential Time Hypothesis, and k-DSH is the hypothesis  ...  We propose the MWC Conjecture, a new conditional hardness conjecture that the weight of a minimum weight cycle in a directed graph cannot be computed in time polynomially smaller than mn.  ...  orthogonal vectors (OV) [11] .  ... 
arXiv:1611.07008v3 fatcat:vuwsyquqn5bwlp2kyx7iks5wxi

Computing top-k Closeness Centrality Faster in Unweighted Graphs [article]

Elisabetta Bergamini, Michele Borassi, Pierluigi Crescenzi, Andrea Marino, Henning Meyerhenke
2017 arXiv   pre-print
on computing the distance between all pairs of vertices, and the state of the art.  ...  This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the k most central vertices has been deeply analysed in the last decade.  ...  solving this problem in O(|C|2− ) would falsify the Orthogonal Vector conjecture.  ... 
arXiv:1704.01077v2 fatcat:gc32wvmmdzhczka6rv7h3c7ajy

Nearly Optimal Average-Case Complexity of Counting Bicliques Under SETH [article]

Shuichi Hirahara, Nobutaka Shimizu
2020 arXiv   pre-print
Then, we amplify the hardness of this problem using the direct product theorem and Yao's XOR lemma by presenting a general framework of hardness amplification in the setting of fine-grained complexity.  ...  In this paper, we seek a natural problem and a natural distribution of instances such that any O(n^c-ϵ)-time algorithm fails to solve most instances drawn from the distribution, while the problem admits  ...  Acknowledgement We thank Marhsall Ball for helpful discussion on Proof of Work. Shuichi Hirahara is supported by ACT-I, JST. Nobutaka Shimizu is supported by JSPS KAKENHI Grant Number JP19J12876.  ... 
arXiv:2010.05822v1 fatcat:zp5fqu4ro5abzethr3bvjwy4jy

Hypercomputation and the Physical Church-Turing Thesis

P. Cotogno
2003 British Journal for the Philosophy of Science  
A version of the Church-Turing Thesis states that every effectively realizable physical system can be defined by Turing Machines ('Thesis P'); in this formulation the Thesis appears an empirical, more  ...  We review the main approaches to computation beyond Turing definability ('hypercomputation'): supertask, non-well-founded, analog, quantum, and retrocausal computation.  ...  Acknowledgements I would like to thank the referees for helpful comments on the earlier version of this paper.  ... 
doi:10.1093/bjps/54.2.181 fatcat:xlui5wr4bfhqfeplrj2e4gdawy

Coarse-Grained Complexity for Dynamic Algorithms [article]

Sayan Bhattacharya, Danupon Nanongkai, Thatchaphol Saranurak
2020 arXiv   pre-print
These arguments rely on strong assumptions about specific problems such as the Strong Exponential Time Hypothesis (SETH) and the Online Matrix-Vector Multiplication Conjecture (OMv).  ...  What if dynamic Orthogonal Vector (OV) is easy in the cell-probe model?  ...  Acknowledgement Nanongkai and Saranurak thank Thore Husfeldt for bringing [HR03]  ... 
arXiv:2001.00336v1 fatcat:5amiy7ibxfgxrlei2ykbirhpzi

Subpath Queries on Compressed Graphs: a Survey [article]

Nicola Prezza
2020 arXiv   pre-print
The earliest optimal-time solution to the problem, the suffix tree, dates back to 1973 and requires up to two orders of magnitude more space than the plain text just to be stored.  ...  Recent trends considered more powerful compression schemes (dictionary compressors) and generalizations of the problem to labeled graphs: after all, texts can be viewed as labeled directed paths.  ...  sparse, a sub-quadratic algorithm for the problem would falsify SETH.  ... 
arXiv:2011.10008v2 fatcat:nbx6tdyurbfexkojuuyzmpr4wu

Subpath Queries on Compressed Graphs: A Survey

Nicola Prezza
2021 Algorithms  
The earliest optimal-time solution to the problem, the suffix tree, dates back to 1973 and requires up to two orders of magnitude more space than the plain text just to be stored.  ...  Recent trends considered more powerful compression schemes (dictionary compressors) and generalizations of the problem to labeled graphs: after all, texts can be viewed as labeled directed paths.  ...  sparse, a subquadratic algorithm for the problem would falsify SETH.  ... 
doi:10.3390/a14010014 fatcat:leysuxakfbdofnnpjnh5xphzcq

On Non-Linear Quantum Mechanics and the Measurement Problem III. Poincare Probability and ... Chaos? [article]

W. David Wick
2018 arXiv   pre-print
required is determined by structural features of the model, and does not require a free parameter.  ...  Paper I of this series introduced a nonlinear version of quantum mechanics that blocks cats, and paper II postulated a random part of the wavefunction to explain outcomes in experiments such as Stern-Gerlach  ...  i ∂t = N j=1 H i,j ψ j . (1) Here I have seth = 1 and ψ is a complex-valued vector of length N .  ... 
arXiv:1803.11236v1 fatcat:xjsvpw64bvfblhlyp6mqnvoati

Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory [article]

Christian Saemann
2006 arXiv   pre-print
Eventually, we present two pairs of matrix models in the context of twistor string theory, and find a relation between the ADHM- and Nahm-constructions and topological D-brane configurations.  ...  We present in detail the case of N=4 super Yang-Mills theory and its self-dual truncation.  ...  However, the complex approach is more geometrical and more natural from the point of view of an action principle and the topological B-model.  ... 
arXiv:hep-th/0603098v1 fatcat:djsbbxsppfdfvibix56p7jckia

Quantum Fluctuations of Vector Fields and the Primordial Curvature Perturbation in the Universe [article]

Mindaugas Karciauskas
2010 arXiv   pre-print
This formalism is applied for two vector curvaton models and the end-of-inflation scenario.  ...  The latter is quantized in de Sitter space-time and it is found that in general the particle production process of the vector field is anisotropic.  ...  The author of the earliest one in Ref. [87] considered three orthogonal identical vector fields.  ... 
arXiv:1009.1779v1 fatcat:x6sah6533rhzphativ7lf2v3pi
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