Editing Hash function (section)

=== Variable range with minimal movement (dynamic hash function) ===
When the hash function is used to store values in a hash table that outlives the run of the program, and the hash table needs to be expanded or shrunk, the hash table is referred to as a dynamic hash table.

A hash function that will relocate the minimum number of records when the table is resized is desirable. What is needed is a hash function {{math|''H''(''z'',''n'')}} (where {{math|''z''}} is the key being hashed and {{math|''n''}} is the number of allowed hash values) such that {{math|1=''H''(''z'',''n''&nbsp;+&nbsp;1) = ''H''(''z'',''n'')}} with probability close to {{math|''n''/(''n''&nbsp;+&nbsp;1)}}.

[[Linear hashing]] and [[spiral hashing]] are examples of dynamic hash functions that execute in constant time but relax the property of uniformity to achieve the minimal movement property. [[Extendible hashing]] uses a dynamic hash function that requires space proportional to {{math|''n''}} to compute the hash function, and it becomes a function of the previous keys that have been inserted. Several algorithms that preserve the uniformity property but require time proportional to {{math|''n''}} to compute the value of {{math|''H''(''z'',''n'')}} have been invented.{{clarify|date=September 2019}}

A hash function with minimal movement is especially useful in [[distributed hash table]]s.