Algorithm 1 Insert(x)

Input.$x,last,Max,k$ Output. true/false   1: $f\leftarrow h_0\left(x\right)$   2: $last\leftarrow \varnothing$   3: for $i\leftarrow 0$ to $Max$ do   4:     calculate hash values $h_1\left(f\right),h_2\left(f\right),\dots ,h_k\left(f\right)$   5:     acquiring buckets $B_1,B_2,\dots ,B_k$ corresponding to hash values from a hash ring   6:     if $\exists B_i(1\le i\le k)$ contains an empty entry e then   7:         $e\leftarrow f$   8:         return true   9:     end if  10:     select a fingerprint e from any bucket $B_i(1\le i\le k,B_i\ne last)$  11:     $f\leftrightarrow e$  12:     $last\leftrightarrow B_i$  13: end for  14: return false