相关论文: Enumeration of sequences with large alphabets

The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…

Next-generation sequencing techniques have facilitated a large scale analysis of human genetic variation. Despite the advances in sequencing speeds, the computational discovery of structural variants is not yet standard. It is likely that…

This paper proposes a binarization scheme for vectors of high dimension based on the recent concept of anti-sparse coding, and shows its excellent performance for approximate nearest neighbor search. Unlike other binarization schemes, this…

We give efficient algorithms for ranking Lyndon words of length $n$ over an alphabet of size $\sigma$. The rank of a Lyndon word is its position in the sequence of lexicographically ordered Lyndon words of the same length. The outputs are…

DNA sequencing is the process of determining the exact order of the nucleotide bases of an individual's genome in order to catalogue sequence variation and understand its biological implications. Whole-genome sequencing techniques produce…

Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…

We initiate the study of computational problems on $k$-mers (strings of length $k$) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct $k$-mers found on the walks of a graph. We establish that…

The at-most-k constraint is ubiquitous in combinatorial problems, and numerous SAT encodings are available for the constraint. Prior experiments have shown the competitiveness of the sequential-counter encoding for k $>$ 1, and have…

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realised by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…

An ensemble method should cleverly combine a group of base classifiers to yield an improved classifier. The majority vote is an example of a methodology used to combine classifiers in an ensemble method. In this paper, we propose to combine…

Getting a robust time-series clustering with best choice of distance measure and appropriate representation is always a challenge. We propose a novel mechanism to identify the clusters combining learned compact representation of…

String Kernel (SK) techniques, especially those using gapped $k$-mers as features (gk), have obtained great success in classifying sequences like DNA, protein, and text. However, the state-of-the-art gk-SK runs extremely slow when we…

The sum capacity on a symbol-synchronous CDMA system having processing gain $N$ and supporting $K$ power constrained users is achieved by employing at most $2N-1$ sequences. Analogously, the minimum received power (energy-per-chip) on the…

We present a collection of new results on problems related to 3SUM, including: 1. The first truly subquadratic algorithm for $\ \ \ \ \ $ 1a. computing the (min,+) convolution for monotone increasing sequences with integer values bounded by…

Recent works have shown that tokenisation is NP-complete. However, these works assume tokenisation is applied to inputs with unboundedly large alphabets -- an unrealistic assumption, given that in practice tokenisers operate over fixed-size…

We consider the following combinatorial question. Let $$ S_0 \subset S_1 \subset S_2 \subset ...\subset S_m $$ be nested sets, where #$(S_i) = i$. A move consists of altering one of the sets $S_i$, $1 \le i \le m-1$, in a manner so that the…

We consider NCA labeling schemes: given a rooted tree $T$, label the nodes of $T$ with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the label of their nearest common…

Varshamov-Tenengolts (VT) codes are a class of codes which can correct a single deletion or insertion with a linear-time decoder. This paper addresses the problem of efficient encoding of non-binary VT codes, defined over an alphabet of…

We present Charagram embeddings, a simple approach for learning character-based compositional models to embed textual sequences. A word or sentence is represented using a character n-gram count vector, followed by a single nonlinear…

Cyclic codes have attracted a lot of research interest for decades. In this paper, for an odd prime $p$, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding…