Hashing: Clarified theorem on complexity of Cuckoo hashing

06-hash/hash.tex

@@ -631,9 +631,11 @@ attempts (this is called insertion timeout), we give up and rehash everything
 with new choice of $f$ and~$g$.
 
 \theorem{
-Let $m\ge (2+\varepsilon)n$, insertion timeout be set to $\lceil 6\log n\rceil$ and
+Let $\varepsilon>0$ be a~fixed constant.
+Suppose that $m\ge (2+\varepsilon)n$, insertion timeout is set to $\lceil 6\log n\rceil$, and
 $f$,~$g$ chosen at random from a~$\lceil 6\log n\rceil$-independent family.
-Then the expected time complexity of \alg{Insert} is $\O(1)$.
+Then the expected time complexity of \alg{Insert} is $\O(1)$, where the constant
+in~$\O$ depends on~$\varepsilon$.
 }
 
 \note{