Cache-Oblivious Implicit Predecessor Dictionaries with the Working Set Property

TL;DR

This paper introduces a cache-oblivious implicit dynamic dictionary supporting efficient predecessor, successor, and search operations with the working-set property, all in worst-case time and using no extra space.

Contribution

It presents the first implicit dictionary with the working-set property supporting predecessor and successor searches efficiently.

Findings

Supports insert and delete in O(log n) time.

Predecessor and successor queries in O(log l) time.

Uses no additional space and is cache-oblivious.

Abstract

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.