Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property

Gerth Stølting Brodal , Casper Kejlberg-Rasmussen

In this paper we present an implicit dynamic dictionary with the working-set property, supporting insert(e) and delete(e) in O(log n) time, predecessor(e) in O(log l_{p(e)}) time, successor(e) in O(log l_{s(e)}) time and search(e) in O(log min(l_{p(e)},l_{e}, l_{s(e)})) time, where n is the number of elements stored in the dictionary, l_{e} is the number of distinct elements searched for since element e was last searched for and p(e) and s(e) are the predecessor and successor of e, respectively. The time-bounds are all worst-case. The dictionary stores the elements in an array of size n using *no* additional space. In the cache-oblivious model the log is base B and the cache-obliviousness is due to our black box use of an existing cache-oblivious implicit dictionary. This is the first implicit dictionary supporting predecessor and successor searches in the working-set bound. Previous implicit structures required O(log n) time.

Mots clés: working-set property; dictionary; implicit; cache-oblivious; worst-case; external memory; I/O efficient

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Gerth Stølting Brodal, Casper Kejlberg-Rasmussen. Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.112-123. ⟨hal-00678181⟩