Unlike the well-known APSP equivalent class, few OV-hard problems are known to be equivalent to OV. In this paper,
we showed several natural problems are equivalent to O(log n) dimensional OV. Two most interesting problems are: approximate
bichromatic closest pair and O(log n) dimensional Maximum Inner Product. In order to get reductions from these problems to OV,
we make use of Sigma_2 communication protocols and Locality Sensitivity Hashing. Our results also apply to the data structure
setting, in which we show that Partial Match and Nearest Neighbor Search are equivalent in a certain sense.