19,251 research outputs found
LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations
LRM-Trees are an elegant way to partition a sequence of values into sorted
consecutive blocks, and to express the relative position of the first element
of each block within a previous block. They were used to encode ordinal trees
and to index integer arrays in order to support range minimum queries on them.
We describe how they yield many other convenient results in a variety of areas,
from data structures to algorithms: some compressed succinct indices for range
minimum queries; a new adaptive sorting algorithm; and a compressed succinct
data structure for permutations supporting direct and indirect application in
time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur
RAM-Efficient External Memory Sorting
In recent years a large number of problems have been considered in external
memory models of computation, where the complexity measure is the number of
blocks of data that are moved between slow external memory and fast internal
memory (also called I/Os). In practice, however, internal memory time often
dominates the total running time once I/O-efficiency has been obtained. In this
paper we study algorithms for fundamental problems that are simultaneously
I/O-efficient and internal memory efficient in the RAM model of computation.Comment: To appear in Proceedings of ISAAC 2013, getting the Best Paper Awar
An Efficient Multiway Mergesort for GPU Architectures
Sorting is a primitive operation that is a building block for countless
algorithms. As such, it is important to design sorting algorithms that approach
peak performance on a range of hardware architectures. Graphics Processing
Units (GPUs) are particularly attractive architectures as they provides massive
parallelism and computing power. However, the intricacies of their compute and
memory hierarchies make designing GPU-efficient algorithms challenging. In this
work we present GPU Multiway Mergesort (MMS), a new GPU-efficient multiway
mergesort algorithm. MMS employs a new partitioning technique that exposes the
parallelism needed by modern GPU architectures. To the best of our knowledge,
MMS is the first sorting algorithm for the GPU that is asymptotically optimal
in terms of global memory accesses and that is completely free of shared memory
bank conflicts.
We realize an initial implementation of MMS, evaluate its performance on
three modern GPU architectures, and compare it to competitive implementations
available in state-of-the-art GPU libraries. Despite these implementations
being highly optimized, MMS compares favorably, achieving performance
improvements for most random inputs. Furthermore, unlike MMS, state-of-the-art
algorithms are susceptible to bank conflicts. We find that for certain inputs
that cause these algorithms to incur large numbers of bank conflicts, MMS can
achieve up to a 37.6% speedup over its fastest competitor. Overall, even though
its current implementation is not fully optimized, due to its efficient use of
the memory hierarchy, MMS outperforms the fastest comparison-based sorting
implementations available to date
Managing Unbounded-Length Keys in Comparison-Driven Data Structures with Applications to On-Line Indexing
This paper presents a general technique for optimally transforming any
dynamic data structure that operates on atomic and indivisible keys by
constant-time comparisons, into a data structure that handles unbounded-length
keys whose comparison cost is not a constant. Examples of these keys are
strings, multi-dimensional points, multiple-precision numbers, multi-key data
(e.g.~records), XML paths, URL addresses, etc. The technique is more general
than what has been done in previous work as no particular exploitation of the
underlying structure of is required. The only requirement is that the insertion
of a key must identify its predecessor or its successor.
Using the proposed technique, online suffix tree can be constructed in worst
case time per input symbol (as opposed to amortized
time per symbol, achieved by previously known algorithms). To our knowledge,
our algorithm is the first that achieves worst case time per input
symbol. Searching for a pattern of length in the resulting suffix tree
takes time, where is the
number of occurrences of the pattern. The paper also describes more
applications and show how to obtain alternative methods for dealing with suffix
sorting, dynamic lowest common ancestors and order maintenance
- …