Methods and apparatus to estimate the second frequency moment for computer-monitored media accesses

A non-transitory computer readable medium comprising computer readable instructions which, when executed, cause a processor to at least:

• in response to a query request, input a first audience member identifier and a second audience member identifier of media impression data through a hashing function, an output being a first bit-value representation of the first audience member identifier and a second bit-value representation of the second audience member identifier;
• increment first and second values of corresponding first and second positions in a vector based on the first and second bit-value representations, respectively;
• estimate a second frequency moment of the media impression data using the vector;
• and
• using the second frequency moment, determine whether the processor can complete the query request of the media impression data based on query processing constraints.

A method to determine whether a computer can complete a query request associated with media impression data based on a second frequency moment of the media impression data, the method comprising:

• in response to the query request, inputting a first audience member identifier and a second audience member identifier of media impression data through a hashing function, an output being a first bit-value representation of the first audience member identifier and a second bit-value representation of the second audience member identifier;
• incrementing first and second values of corresponding first and second positions in a vector based on the first and second bit-value representations, respectively;
• estimating the second frequency moment of the media impression data using the vector;
• and
• using the second frequency moment, determining whether the computer can complete the query request of the media impression data based on query processing constraints.