+\begin{frame}{MurmurHash3 -- properties}
+ \begin{itemize}
+ \item Simple
+ \item Good distribution
+ \item Good collision resistance
+ \item Good avalanche properties (single bit in the input changes the output significantly).
+ \only<2>{\begin{itemize}
+ \item 0 -> {\texttt \Sexpr{digest::digest(0,"sha1")}}
+ \item 1 -> {\texttt \Sexpr{digest::digest(1,"sha1")}}
+ \item 2 -> {\texttt \Sexpr{digest::digest(2,"sha1")}}
+ \end{itemize}}
+ \item<3-> Fast
+ \item<3-> Key questions:
+ \begin{enumerate}
+ \item Does it map DNA and protein sequences uniformly into output?
+ \item Does the non-random input distribution of DNA/protein
+ sequences expose pathologic behavior of the hash function?
+ \end{enumerate}
+ \item<3-> Partially answered by the smhasher test suite which
+ exposed issues with MurmurHash2 (which is ideally the
+ \href{http://www.phy.duke.edu/\%7Ergb/General/dieharder.php}{DieHarder}
+ of hash testing.)
+ \end{itemize}