Primary clustering

In computer programming, primary clustering is a phenomenon that causes performance degradation in linear probing hash tables. The phenomenon states that, as elements are added to a linear probing hash table, they have a tendency to cluster together into long runs (i. e., long contiguous regions of the hash table that contain no free slots). If the hash table is at a load factor of for some parameter , then the expected length of the run containing a given element is This causes insertions and negative queries to take expected time in a linear probing hash table.

Primary clustering causes performance degradation for both insertions and queries in a linear probing hash table. Insertions must travel to the end of a run, and therefore take expected time However, as noted by Knuth, typically citing Knuth. (often referred to as Robin Hood hashing) is a technique for reducing the effects of primary clustering on queries. Ordered linear probing sorts the elements within each run by their hash. Thus, a query can terminate as soon as it encounters any element whose hash is larger than that of the element being queried. This results in both positive and negative queries taking expected time
Graveyard hashing is a variant of ordered linear probing that eliminates the asymptotic effects of primary clustering for all operations. Graveyard hashing strategically leaves gaps within runs that future insertions can make use of. These gaps, which can be thought of as tombstones (like those created by lazy deletions), are inserted into the table during semi regular rebuilds. The gaps then speed up the insertions that take place until the next semi regular rebuild occurs. Every operation in a graveyard hash table takes expected time
Many sources recommend the use of quadratic probing as an alternative to linear probing that empirically avoids the effects of primary clustering.