2 research outputs found
Tight Cell Probe Bounds for Succinct Boolean Matrix-Vector Multiplication
The conjectured hardness of Boolean matrix-vector multiplication has been
used with great success to prove conditional lower bounds for numerous
important data structure problems, see Henzinger et al. [STOC'15]. In recent
work, Larsen and Williams [SODA'17] attacked the problem from the upper bound
side and gave a surprising cell probe data structure (that is, we only charge
for memory accesses, while computation is free). Their cell probe data
structure answers queries in time and is succinct in the
sense that it stores the input matrix in read-only memory, plus an additional
bits on the side. In this paper, we essentially settle the
cell probe complexity of succinct Boolean matrix-vector multiplication. We
present a new cell probe data structure with query time
storing just bits on the side. We then complement our data
structure with a lower bound showing that any data structure storing bits
on the side, with must have query time satisfying . For , any data structure must have . Since lower bounds in the cell probe model also apply to
classic word-RAM data structures, the lower bounds naturally carry over. We
also prove similar lower bounds for matrix-vector multiplication over