Faster Sparse Suffix Sorting

The sparse suffix sorting problem is to sort b=o(n) arbitrary suffixes of a string of length n using o(n) words of space in addition to the string. We present an O(n) time Monte Carlo algorithm using O(b.log(b)) space and an O(n.log(b)) time Las Vegas algorithm using O(b) space. This is a significant improvement over the best prior solutions of [Bille et al., ICALP 2013]: a Monte Carlo algorithm running in O(n.log(b)) time and O(b^(1+e)) space or O(n.log^2(b)) time and O(b) space, and a Las Vegas algorithm running in O(n.log^2(b)+b^2.log(b)) time and O(b) space. All the above results are obtained with high probability not just in expectation

Optimal Substring-Equality Queries with Applications to Sparse Text Indexing

We consider the problem of encoding a string of length $n$ from an integer alphabet of size $\sigma$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any uniquely-decodable encoding supporting access must take $n\log\sigma + \Theta(\log (n\log\sigma))$ bits. We describe a new data structure matching this lower bound when $\sigma\leq n^{O(1)}$ while supporting both queries in optimal $O(1)$ time. Furthermore, we show that the string can be overwritten in-place with this structure. The redundancy of $\Theta(\log n)$ bits and the constant query time break exponentially a lower bound that is known to hold in the read-only model. Using our new string representation, we obtain the first in-place subquadratic (indeed, even sublinear in some cases) algorithms for several string-processing problems in the restore model: the input string is rewritable and must be restored before the computation terminates. In particular, we describe the first in-place subquadratic Monte Carlo solutions to the sparse suffix sorting, sparse LCP array construction, and suffix selection problems. With the sole exception of suffix selection, our algorithms are also the first running in sublinear time for small enough sets of input suffixes. Combining these solutions, we obtain the first sublinear-time Monte Carlo algorithm for building the sparse suffix tree in compact space. We also show how to derandomize our algorithms using small space. This leads to the first Las Vegas in-place algorithm computing the full LCP array in $O(n\log n)$ time and to the first Las Vegas in-place algorithms solving the sparse suffix sorting and sparse LCP array construction problems in $O(n^{1.5}\sqrt{\log \sigma})$ time. Running times of these Las Vegas algorithms hold in the worst case with high probability.Comment: Refactored according to TALG's reviews. New w.h.p. bounds and Las Vegas algorithm

CiNCT: Compression and retrieval for massive vehicular trajectories via relative movement labeling

In this paper, we present a compressed data structure for moving object trajectories in a road network, which are represented as sequences of road edges. Unlike existing compression methods for trajectories in a network, our method supports pattern matching and decompression from an arbitrary position while retaining a high compressibility with theoretical guarantees. Specifically, our method is based on FM-index, a fast and compact data structure for pattern matching. To enhance the compression, we incorporate the sparsity of road networks into the data structure. In particular, we present the novel concepts of relative movement labeling and PseudoRank, each contributing to significant reductions in data size and query processing time. Our theoretical analysis and experimental studies reveal the advantages of our proposed method as compared to existing trajectory compression methods and FM-index variants

Deterministic sub-linear space LCE data structures with efficient construction

Given a string $S$ of $n$ symbols, a longest common extension query $\mathsf{LCE}(i,j)$ asks for the length of the longest common prefix of the $i$th and $j$th suffixes of $S$. LCE queries have several important applications in string processing, perhaps most notably to suffix sorting. Recently, Bille et al. (J. Discrete Algorithms 25:42-50, 2014, Proc. CPM 2015: 65-76) described several data structures for answering LCE queries that offers a space-time trade-off between data structure size and query time. In particular, for a parameter $1 \leq \tau \leq n$, their best deterministic solution is a data structure of size $O(n/\tau)$ which allows LCE queries to be answered in $O(\tau)$ time. However, the construction time for all deterministic versions of their data structure is quadratic in $n$. In this paper, we propose a deterministic solution that achieves a similar space-time trade-off of $O(\tau\min\{\log\tau,\log\frac{n}{\tau}\})$ query time using $O(n/\tau)$ space, but significantly improve the construction time to $O(n\tau)$.Comment: updated titl

The Parallelism Motifs of Genomic Data Analysis

Genomic data sets are growing dramatically as the cost of sequencing continues to decline and small sequencing devices become available. Enormous community databases store and share this data with the research community, but some of these genomic data analysis problems require large scale computational platforms to meet both the memory and computational requirements. These applications differ from scientific simulations that dominate the workload on high end parallel systems today and place different requirements on programming support, software libraries, and parallel architectural design. For example, they involve irregular communication patterns such as asynchronous updates to shared data structures. We consider several problems in high performance genomics analysis, including alignment, profiling, clustering, and assembly for both single genomes and metagenomes. We identify some of the common computational patterns or motifs that help inform parallelization strategies and compare our motifs to some of the established lists, arguing that at least two key patterns, sorting and hashing, are missing