We consider the approximate nearest neighbour search problem on the
Hamming Cube $\b^d$. We show that a randomised cell probe algorithm that
uses polynomial storage and word size $d^{O(1)}$ requires a worst case
query time of $\Omega(\log\log d/\log\log\log d)$. The approximation
factor may be as loose as $2^{\log^{1-\eta}d}$ for any ... more >>>

SBP is a probabilistic promise class located
between MA and AM \cap BPPpath. The first
part of the paper studies the question of whether
SBP has many-one complete sets. We relate
this question to the existence of uniform
enumerations. We construct an oracle relative to
which SBP and AM do ... more >>>

We prove the first lower bound for restricted read-once parity branching
programs with unlimited parity nondeterminism where for each input the
variables may be tested according to several orderings.

Proving a superpolynomial lower bound for read-once parity branching
programs is still a challenging open problem. The following variant ... more >>>