  This paper establishes the theoretical framework of b-bit minwise hashing.
The original minwise hashing method has become a standard technique for
estimating set similarity (e.g., resemblance) with applications in information
retrieval, data management, social networks and computational advertising.
  By only storing the lowest $b$ bits of each (minwise) hashed value (e.g., b=1
or 2), one can gain substantial advantages in terms of computational efficiency
and storage space. We prove the basic theoretical results and provide an
unbiased estimator of the resemblance for any b. We demonstrate that, even in
the least favorable scenario, using b=1 may reduce the storage space at least
by a factor of 21.3 (or 10.7) compared to using b=64 (or b=32), if one is
interested in resemblance > 0.5.
