Editing Perfect hash function (section)

==Performance of perfect hash functions==
The important performance parameters for perfect hashing are the representation size, the evaluation time, the construction time, and additionally the range requirement <math>\frac{m}{n}</math> (average number of buckets per key in the hash table).<ref name="CHD"/> The evaluation time can be as fast as {{math|''O''(''1'')}}, which is optimal.<ref name="inventor"/><ref name="CHD"/> The construction time needs to be at least {{math|''O''(''n'')}}, because each element in {{mvar|S}} needs to be considered, and {{mvar|S}} contains {{mvar|n}} elements. This lower bound can be achieved in practice.<ref name="CHD"/>

The lower bound for the representation size depends on {{mvar|m}} and {{mvar|n}}. Let {{math|''m'' {{=}} (1+&epsilon;) ''n''}} and {{mvar|h}} a perfect hash function. A good approximation for the lower bound is <math>\log e - \varepsilon \log \frac{1+\varepsilon}{\varepsilon}</math> Bits per element. For minimal perfect hashing, {{math|&epsilon; {{=}} 0}}, the lower bound is {{math|log e ≈ 1.44}} bits per element.<ref name="CHD"/>