13,967 research outputs found
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
Incremental dimension reduction of tensors with random index
We present an incremental, scalable and efficient dimension reduction
technique for tensors that is based on sparse random linear coding. Data is
stored in a compactified representation with fixed size, which makes memory
requirements low and predictable. Component encoding and decoding are performed
on-line without computationally expensive re-analysis of the data set. The
range of tensor indices can be extended dynamically without modifying the
component representation. This idea originates from a mathematical model of
semantic memory and a method known as random indexing in natural language
processing. We generalize the random-indexing algorithm to tensors and present
signal-to-noise-ratio simulations for representations of vectors and matrices.
We present also a mathematical analysis of the approximate orthogonality of
high-dimensional ternary vectors, which is a property that underpins this and
other similar random-coding approaches to dimension reduction. To further
demonstrate the properties of random indexing we present results of a synonym
identification task. The method presented here has some similarities with
random projection and Tucker decomposition, but it performs well at high
dimensionality only (n>10^3). Random indexing is useful for a range of complex
practical problems, e.g., in natural language processing, data mining, pattern
recognition, event detection, graph searching and search engines. Prototype
software is provided. It supports encoding and decoding of tensors of order >=
1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure
Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation
Given a static reference string and a source string , a relative
compression of with respect to is an encoding of as a sequence of
references to substrings of . Relative compression schemes are a classic
model of compression and have recently proved very successful for compressing
highly-repetitive massive data sets such as genomes and web-data. We initiate
the study of relative compression in a dynamic setting where the compressed
source string is subject to edit operations. The goal is to maintain the
compressed representation compactly, while supporting edits and allowing
efficient random access to the (uncompressed) source string. We present new
data structures that achieve optimal time for updates and queries while using
space linear in the size of the optimal relative compression, for nearly all
combinations of parameters. We also present solutions for restricted and
extended sets of updates. To achieve these results, we revisit the dynamic
partial sums problem and the substring concatenation problem. We present new
optimal or near optimal bounds for these problems. Plugging in our new results
we also immediately obtain new bounds for the string indexing for patterns with
wildcards problem and the dynamic text and static pattern matching problem
Compressed Text Indexes:From Theory to Practice!
A compressed full-text self-index represents a text in a compressed form and
still answers queries efficiently. This technology represents a breakthrough
over the text indexing techniques of the previous decade, whose indexes
required several times the size of the text. Although it is relatively new,
this technology has matured up to a point where theoretical research is giving
way to practical developments. Nonetheless this requires significant
programming skills, a deep engineering effort, and a strong algorithmic
background to dig into the research results. To date only isolated
implementations and focused comparisons of compressed indexes have been
reported, and they missed a common API, which prevented their re-use or
deployment within other applications.
The goal of this paper is to fill this gap. First, we present the existing
implementations of compressed indexes from a practitioner's point of view.
Second, we introduce the Pizza&Chili site, which offers tuned implementations
and a standardized API for the most successful compressed full-text
self-indexes, together with effective testbeds and scripts for their automatic
validation and test. Third, we show the results of our extensive experiments on
these codes with the aim of demonstrating the practical relevance of this novel
and exciting technology
Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties
The shape of irregular particles has significant influence on micro- and
macro-scopic behavior of granular systems. This paper presents a combined 3D
thinning and greedy set-covering algorithm to approximate realistic particles
with a clump of overlapping spheres for discrete element method (DEM)
simulations. First, the particle medial surface (or surface skeleton), from
which all candidate (maximal inscribed) spheres can be generated, is computed
by the topological 3D thinning. Then, the clump generation procedure is
converted into a greedy set-covering (SCP) problem.
To correct the mass distribution due to highly overlapped spheres inside the
clump, linear programming (LP) is used to adjust the density of each component
sphere, such that the aggregate properties mass, center of mass and inertia
tensor are identical or close enough to the prototypical particle. In order to
find the optimal approximation accuracy (volume coverage: ratio of clump's
volume to the original particle's volume), particle flow of 3 different shapes
in a rotating drum are conducted. It was observed that the dynamic angle of
repose starts to converge for all particle shapes at 85% volume coverage
(spheres per clump < 30), which implies the possible optimal resolution to
capture the mechanical behavior of the system.Comment: 34 pages, 13 figure
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