24 research outputs found
String Synchronizing Sets: Sublinear-Time BWT Construction and Optimal LCE Data Structure
Burrows-Wheeler transform (BWT) is an invertible text transformation that,
given a text of length , permutes its symbols according to the
lexicographic order of suffixes of . BWT is one of the most heavily studied
algorithms in data compression with numerous applications in indexing, sequence
analysis, and bioinformatics. Its construction is a bottleneck in many
scenarios, and settling the complexity of this task is one of the most
important unsolved problems in sequence analysis that has remained open for 25
years. Given a binary string of length , occupying machine
words, the BWT construction algorithm due to Hon et al. (SIAM J. Comput., 2009)
runs in time and space. Recent advancements (Belazzougui,
STOC 2014, and Munro et al., SODA 2017) focus on removing the alphabet-size
dependency in the time complexity, but they still require time.
In this paper, we propose the first algorithm that breaks the -time
barrier for BWT construction. Given a binary string of length , our
procedure builds the Burrows-Wheeler transform in time and
space. We complement this result with a conditional lower bound
proving that any further progress in the time complexity of BWT construction
would yield faster algorithms for the very well studied problem of counting
inversions: it would improve the state-of-the-art -time
solution by Chan and P\v{a}tra\c{s}cu (SODA 2010). Our algorithm is based on a
novel concept of string synchronizing sets, which is of independent interest.
As one of the applications, we show that this technique lets us design a data
structure of the optimal size that answers Longest Common
Extension queries (LCE queries) in time and, furthermore, can be
deterministically constructed in the optimal time.Comment: Full version of a paper accepted to STOC 201
Efficient Computation of Sequence Mappability
Sequence mappability is an important task in genome re-sequencing. In the
-mappability problem, for a given sequence of length , our goal
is to compute a table whose th entry is the number of indices such
that length- substrings of starting at positions and have at
most mismatches. Previous works on this problem focused on heuristic
approaches to compute a rough approximation of the result or on the case of
. We present several efficient algorithms for the general case of the
problem. Our main result is an algorithm that works in time and space for
. It requires a carefu l adaptation of the technique of Cole
et al.~[STOC 2004] to avoid multiple counting of pairs of substrings. We also
show -time algorithms to compute all results for a fixed
and all or a fixed and all . Finally we show
that the -mappability problem cannot be solved in strongly subquadratic
time for unless the Strong Exponential Time Hypothesis
fails.Comment: Accepted to SPIRE 201
Finding the Anticover of a String
A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k ? 3. We also show that the problem admits a polynomial-time solution for k=2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O*(min {3^{(n-k)/3)}, ((k(k+1))/2)^{n/(k+1)) time using polynomial space
IUPACpal: efficient identification of inverted repeats in IUPAC-encoded DNA sequences
Background: An inverted repeat is a DNA sequence followed downstream by its reverse complement, potentially with a gap in the centre. Inverted repeats are found in both prokaryotic and eukaryotic genomes and they have been linked with countless possible functions. Many international consortia provide a comprehensive description of common genetic variation making alternative sequence representations, such as IUPAC encoding, necessary for leveraging the full potential of such broad variation datasets. Results: We present IUPACpal, an exact tool for efficient identification of inverted repeats in IUPAC-encoded DNA sequences allowing also for potential mismatches and gaps in the inverted repeats. Conclusion: Within the parameters that were tested, our experimental results show that IUPACpal compares favourably to a similar application packaged with EMBOSS. We show that IUPACpal identifies many previously unidentified inverted repeats when compared with EMBOSS, and that this is also performed with orders of magnitude improved speed.</p
Comparing Degenerate Strings
Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string S is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1,... , kn-1. Our main result is an (N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in S in (min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in S. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach
Dynamic IoT Malware Detection in Android Systems Using Profile Hidden Markov Models
The prevalence of malware attacks that target IoT systems has raised an alarm and highlighted the need for efficient mechanisms to detect and defeat them. However, detecting malware is challenging, especially malware with new or unknown behaviors. The main problem is that malware can hide, so it cannot be detected easily. Furthermore, information about malware families is limited which restricts the amount of âbig dataâ that is available for analysis. The motivation of this paper is two-fold. First, to introduce a new Profile Hidden Markov Model (PHMM) that can be used for both app analysis and classification in Android systems. Second, to dynamically identify suspicious calls while reducing infection risks of executed codes. We focused on Android systems, as they are more vulnerable than other IoT systems due to their ubiquitousness and sideloading features. The experimental results showed that the proposed Dynamic IoT malware Detection in Android Systems using PHMM (DIP) achieved superior performance when benchmarked against eight rival malware detection frameworks, showing up to 96.3% accuracy at 5% False Positive Rate (FP rate), 3% False Negative Rate (FN rate) and 94.9% F-measure