 
Summary: Ranged Hash Functions and the Price of Churn
James Aspnes
Muli Safra
Yitong Yin§
Abstract
Ranged hash functions generalize hash tables to the set
ting 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 connec
tions. Monotone ranged hash functions are a particular
class of ranged hash functions that minimize item reas
signments in response to churn: changes in the set of
available buckets. The canonical example of a mono
tone ranged hash function is the ringbased 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
