Lazy Kronecker Product

Abstract

In this paper, we show how to generalize the lazy update regime from dynamic matrix product [Cohen, Lee, Song STOC 2019, JACM 2021] to dynamic kronecker product. We provide an algorithm that uses $n^{\omega( \lceil k/2 \rceil, \lfloor k/2 \rfloor, a )-a}$ amortized update time and $ n^{\omega( \lceil(k-s)/2 \rceil, \lfloor (k-s)/2 \rfloor,a )}$ worst case query time for dynamic kronecker product problem. Unless tensor MV conjecture is false, there is no algorithm that can use both $n^{\omega( \lceil k/2 \rceil, \lfloor k/2 \rfloor, a )-a-\Omega(1)}$ amortized update time, and $ n^{\omega( \lceil(k-s)/2 \rceil, \lfloor (k-s)/2 \rfloor,a )-\Omega(1)}$ worst case query time.