2
$\begingroup$

There is an information theoretic lower bound of $\log_2 {U \choose x}$ for the number of bits to represent a subset of $x$ elements chosen from a universe of size $U$. We can in principle use this representation (perhaps inefficiently) as a data structure to test if any query is part of this subset.

How can you show a similar information theoretic lower bound if we are happy to have false positives with some probability $p$?

|cite|improve this question
$\endgroup$
  • $\begingroup$ If you are happy to allow false positives, you are interested in a data structure called Bloom Filters, though sadly I am not familiar with the lower-bound in that framework. $\endgroup$ – user340082710 Jan 29 '15 at 14:12
2
$\begingroup$

In "Network applications of Bloom filters: A survey", Broder and Mitzenmacher show an $x \log_2 (1/p)$ lower bound on the space usage.

|cite|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.