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.Comment: An extended abstract is accepted at STACS 2012, this is the full
version of that paper with the same name "Cache-Oblivious Implicit
Predecessor Dictionaries with the Working-Set Property", Symposium on
Theoretical Aspects of Computer Science 201
