May want to do certain search operations over priority values.
Want to do priority-queue type operations: what is the next-largest integer?

##### Operations

success(q)

Find input object with key > q, as close as possible

if q > top key: abort, no such item

if z ⇐ bottom key, return bottom item

##### Solutions

#### van Embde Boas Tree

Recursive tree structure for integer searching. Base case is any other search method. Current iteration stores min, max values and a hash function into $O(i)$ recursive structures. Record with key $x$ goes into subset $S_{hi(x)}$.
Time bound depends on N, the range of possible keys,

e.g. van Emde Boas tree [Kaas, Zijkstia '76] which are O(log log N) per operation:

i-bit binary number x

(i = 8) 11011110

upper half of x (i/2 bits, hi(x)):

x » (i/2) == 1101

lower half of x (i/2 bits, lo(x)):

x & ^{1)}