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 $T$ of length $n$, permutes its symbols according to the lexicographic order of suffixes of $T$. 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 $n$, occupying $O(n/\log n)$ machine words, the BWT construction algorithm due to Hon et al. (SIAM J. Comput., 2009) runs in $O(n)$ time and $O(n/\log n)$ 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 $\Omega(n)$ time. In this paper, we propose the first algorithm that breaks the $O(n)$-time barrier for BWT construction. Given a binary string of length $n$, our procedure builds the Burrows-Wheeler transform in $O(n/\sqrt{\log n})$ time and $O(n/\log n)$ 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 $O(m\sqrt{\log m})$-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 $O(n/\log n)$ that answers Longest Common Extension queries (LCE queries) in $O(1)$ time and, furthermore, can be deterministically constructed in the optimal $O(n/\log n)$ time.Comment: Full version of a paper accepted to STOC 201

Improved description of charged Higgs boson production at hadron colliders

We present a new method for matching the two twin-processes gb->H+/-t and gg->H+/-tb in Monte Carlo event generators. The matching is done by defining a double-counting term, which is used to generate events that are subtracted from the sum of these two twin-processes. In this way we get a smooth transition between the collinear region of phase space, which is best described by gb->H+/-t, and the hard region, which requires the use of the gg->H+/-tb process. The resulting differential distributions show large differences compared to both the gb-> H+/-t and gg->H+/-tb processes illustrating the necessity to use matching when tagging the accompanying b-jet.Comment: 21 pages, 9 figures. Revised with updated discussion and reference

ThepotentialofDNAasatrulyparallelcomputingdeviceisenormous.Solution-phaseDNAchem-

feasibility,however,iscontroversial.WehavesoughttoextendthefeasibilityandgeneralityofDNA istry,thoughnotunlimited,providestheonlycurrently-availableexperimentalsystem.Itspractical computingbyanovelapplicationofthetheoryofcounting.Thebiochemicallyequivalentoperationfo