Ranged hash functions and the price of churn

Ranged hash functions generalize hash tables to the setting where hash buckets may come and go over time, a typical case in distributed settings where hash buckets may correspond to unreliable servers or network connections. Monotone ranged hash functions are a particular class of ranged hash functions that minimize item reassignments in response to churn: changes in the set of available buckets. The canonical example of a monotone ranged hash function is the ring-based consistent hashing mechanism of Karger et al. [13]. These hash functions give a maximum load of n m log m when n is the number of items and m is the number of buckets. The question of whether some better bound could be obtained using a more sophisticated hash function has remained open. We resolve this question by showing two lower bounds. First, the maximum load of any randomized monotone ranged hash function is ( n m ln m) when n = o(m log m). This bound covers almost all of the nontrivial case, because when n = (m ...

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: James Aspnes, Muli Safra, Yitong Yin
• Keywords: Algorithms, Hash Buckets, Monotone Ranged Hash, Ranged Hash Functions, SODA 2008