5 papers
Online Orthogonal Vectors Revisited
Karthik Gajulapalli, Alexander Golovnev, Samuel King +1
We prove new upper and lower bounds for the Online Orthogonal Vectors Problem (). In this problem, a preprocessing algorithm receives vectors $x_1,\ldo…
Oblivious Complexity Classes Revisited: Lower Bounds and Hierarchies
Karthik Gajulapalli, Zeyong Li, Ilya Volkovich
In this work we study oblivious complexity classes. These classes capture the power of interactive proofs where the prover(s) are only given the input size rather than the actual i…
Output-Sparse Matrix Multiplication Using Compressed Sensing
Huck Bennett, Karthik Gajulapalli, Alexander Golovnev +1
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two matrices when their product is promised to have at mo…
Downward self-reducibility in the total function polynomial hierarchy
Karthik Gajulapalli, Surendra Ghentiyala, Zeyong Li +1
A problem is considered downward self-reducible, if there exists an efficient algorithm for that is allowed to make queries to only strictly smaller ins…
Matrix Multiplication Verification Using Coding Theory
Huck Bennett, Karthik Gajulapalli, Alexander Golovnev +1
We study the Matrix Multiplication Verification Problem (MMV) where the goal is, given three matrices , , and as input, to decide whether . A classic…