Affiliation:
1. Uppsala University, Uppsala, Sweden
2. AT&T Labs--Research, Florham Park, New Jersey
Abstract
We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures.
This leads to an
optimal
bound of
O
(√log
n
/log log
n
) for searching and updating a dynamic set
X
of
n
integer keys in linear space. Searching
X
for an integer
y
means finding the maximum key in
X
which is smaller than or equal to
y
. This problem is equivalent to the standard text book problem of maintaining an ordered set.
The best previous deterministic linear space bound was
O
(log
n
/log log
n
) due to Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space.
We also get the following worst-case linear space trade-offs between the number
n
, the word length
W
, and the maximal key
U
< 2
W
:
O
(min log log
n
+ log
n
/log
W
, log log
n
⋅ log log
U
/log log log
U
). These trade-offs are, however, not likely to be optimal.
Our results are generalized to finger searching and string searching, providing optimal results for both in terms of
n
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
60 articles.
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