68 research outputs found
Decomposability of DiSAT for Index Dynamization
The Distal Spatial Approximation Tree (DiSAT) is one of the most competitive indexes for exact proximity searching. The absence of parameters, the most salient feature, makes the index a suitable choice for a practitioner. The most serious drawback is the static nature of the index, not allowing further insertions once it is built. On the other hand, there is an old approach from Bentley and Saxe (BS) allowing the dynamization of decomposable data structures. The only requirement is to provide a decomposition operation.
This is precisely our contribution, we define a decomposition operation allowing the application of the BS technique. The resulting data structure is competitive against the static counterparts.Facultad de Informátic
A Framework for Index Bulk Loading and Dynamization
In this paper we investigate automated methods for externalizing
internal memory data structures. We consider a class of balanced trees that we
call weight-balanced partitioning trees (or wp-trees) for indexing a set of points
in Rd. Well-known examples of wp-trees include fed-trees, BBD-trees, pseudo
quad trees, and BAR trees. These trees are defined with fixed degree and are
thus suited for internal memory implementations. Given an efficient wp-tree
construction algorithm, we present a general framework for automatically obtaining
a new dynamic external data structure. Using this framework together
with a new general construction (bulk loading) technique of independent interest,
we obtain data structures with guaranteed good update performance in
terms of I /O transfers. Our approach gives considerably improved construction
and update I/O bounds of e.g. fed-trees and BBD-trees
Lower Bounds for Oblivious Near-Neighbor Search
We prove an lower bound on the dynamic
cell-probe complexity of statistically
approximate-near-neighbor search () over the -dimensional
Hamming cube. For the natural setting of , our result
implies an lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
. This is the first super-logarithmic
lower bound for against general (non black-box) data structures.
We also show that any oblivious data structure for
decomposable search problems (like ) can be obliviously dynamized
with overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page
Data structures
We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case
Dynamic Data Structures for Document Collections and Graphs
In the dynamic indexing problem, we must maintain a changing collection of
text documents so that we can efficiently support insertions, deletions, and
pattern matching queries. We are especially interested in developing efficient
data structures that store and query the documents in compressed form. All
previous compressed solutions to this problem rely on answering rank and select
queries on a dynamic sequence of symbols. Because of the lower bound in
[Fredman and Saks, 1989], answering rank queries presents a bottleneck in
compressed dynamic indexing. In this paper we show how this lower bound can be
circumvented using our new framework. We demonstrate that the gap between
static and dynamic variants of the indexing problem can be almost closed. Our
method is based on a novel framework for adding dynamism to static compressed
data structures. Our framework also applies more generally to dynamizing other
problems. We show, for example, how our framework can be applied to develop
compressed representations of dynamic graphs and binary relations
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Fully dynamic maintenance of euclidean minimum spanning trees
We maintain the minimum spanning tree of a point set in the plane, subject to point insertions and deletions, in time O(n^5/6 log1^2/2 n) per update operation. No nontrivial dynamic geometric minimum spanning tree algorithm was previously known. We reduce the problem to maintaining bichromatic closest pairs, which we also solve in the same time bounds. Our algorithm uses a novel construction, the ordered nearest neighbors of a sequence of points. Any point set or bichromatic point set can be ordered so that this graph is a simple path
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