35,213 research outputs found
Computing LZ77 in Run-Compressed Space
In this paper, we show that the LZ77 factorization of a text T {\in\Sigma^n}
can be computed in O(R log n) bits of working space and O(n log R) time, R
being the number of runs in the Burrows-Wheeler transform of T reversed. For
extremely repetitive inputs, the working space can be as low as O(log n) bits:
exponentially smaller than the text itself. As a direct consequence of our
result, we show that a class of repetition-aware self-indexes based on a
combination of run-length encoded BWT and LZ77 can be built in asymptotically
optimal O(R + z) words of working space, z being the size of the LZ77 parsing
A Concurrency-Optimal Binary Search Tree
The paper presents the first \emph{concurrency-optimal} implementation of a
binary search tree (BST). The implementation, based on a standard sequential
implementation of an internal tree, ensures that every \emph{schedule} is
accepted, i.e., interleaving of steps of the sequential code, unless
linearizability is violated. To ensure this property, we use a novel read-write
locking scheme that protects tree \emph{edges} in addition to nodes.
Our implementation outperforms the state-of-the art BSTs on most basic
workloads, which suggests that optimizing the set of accepted schedules of the
sequential code can be an adequate design principle for efficient concurrent
data structures
3D environment mapping using the Kinect V2 and path planning based on RRT algorithms
This paper describes a 3D path planning system that is able to provide a solution trajectory for the automatic control of a robot. The proposed system uses a point cloud obtained from the robot workspace, with a Kinect V2 sensor to identify the interest regions and the obstacles of the environment. Our proposal includes a collision-free path planner based on the Rapidly-exploring Random Trees variant (RRT*), for a safe and optimal navigation of robots in 3D spaces. Results on RGB-D segmentation and recognition, point cloud processing, and comparisons between different RRT* algorithms, are presented.Peer ReviewedPostprint (published version
In pursuit of the dynamic optimality conjecture
In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting
binary search tree algorithm. Splay trees were conjectured to perform within a
constant factor as any offline rotation-based search tree algorithm on every
sufficiently long sequence---any binary search tree algorithm that has this
property is said to be dynamically optimal. However, currently neither splay
trees nor any other tree algorithm is known to be dynamically optimal. Here we
survey the progress that has been made in the almost thirty years since the
conjecture was first formulated, and present a binary search tree algorithm
that is dynamically optimal if any binary search tree algorithm is dynamically
optimal.Comment: Preliminary version of paper to appear in the Conference on Space
Efficient Data Structures, Streams and Algorithms to be held in August 2013
in honor of Ian Munro's 66th birthda
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
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