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REPORTS > KEYWORD > ORTHOGONAL VECTORS:
Reports tagged with orthogonal vectors:
TR16-053 | 6th April 2016
Jiawei Gao, Russell Impagliazzo

#### Orthogonal Vectors is hard for first-order properties on sparse graphs

Revisions: 3

Fine-grained reductions, introduced by Vassilevska-Williams and Williams, preserve any improvement in the known algorithms. These have been used very successfully in relating the exact complexities of a wide range of problems, from NP-complete problems like SAT to important quadratic time solvable problems within P such as Edit Distance. However, until ... more >>>

TR17-170 | 6th November 2017

#### Simulation Beats Richness: New Data-Structure Lower Bounds

We develop a technique for proving lower bounds in the setting of asymmetric communication, a model that was introduced in the famous works of Miltersen (STOC'94) and Miltersen, Nisan, Safra and Wigderson (STOC'95). At the core of our technique is a novel simulation theorem: Alice gets a $p \times n$ ... more >>>

TR18-092 | 4th May 2018
Marco Carmosino, Russell Impagliazzo, Manuel Sabin

#### Fine-Grained Derandomization: From Problem-Centric to Resource-Centric Complexity

We show that popular hardness conjectures about problems from the field of fine-grained complexity theory imply structural results for resource-based complexity classes. Namely, we show that if either k-Orthogonal Vectors or k-CLIQUE requires $n^{\epsilon k}$ time, for some constant $\epsilon > 1/2$, to count (note that these conjectures are significantly ... more >>>

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