Related papers: Constrained de Bruijn Codes: Properties, Enumerati…
A de Bruijn sequence of order $k$ over a finite alphabet is a cyclic sequence with the property that it contains every possible $k$-sequence as a substring exactly once. Orthogonal de Bruijn sequences are collections of de Bruijn sequences…
Motivated by the work on the domination number of directed de Bruijn graphs and some of its generalizations, in this paper we introduce a natural generalization of de Bruijn graphs (directed and undirected), namely $t$-constrained de Bruijn…
The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the…
Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…
Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…
A de Bruijn array code is a set of $r \times s$ binary doubly-periodic arrays such that each binary $n \times m$ matrix is contained exactly once as a window in one of the arrays. Such a set of arrays can be viewed as a two-dimensional…
A de Bruijn sequence of order n over a k-symbol alphabet is a circular sequence where each length-n sequence occurs exactly once. We present a way of extending de Bruijn sequences by adding a new symbol to the alphabet: the extension is…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
We present sufficient conditions for when an ordering of universal cycles $\alpha_1, \alpha_2, \ldots, \alpha_m$ for disjoint sets $\mathbf{S}_1, \mathbf{S}_2, \ldots , \mathbf{S}_m$ can be concatenated together to obtain a universal cycle…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
Classic cycle-joining techniques have found widespread application in creating universal cycles for a diverse range of combinatorial objects, such as shorthand permutations, weak orders, orientable sequences, and various subsets of $k$-ary…
Motivated by applications in DNA-based data storage, constrained codes have attracted a considerable amount of attention from both academia and industry. We study the maximum cardinality of constrained codes for which the constraints can be…
De Bruijn graph is one of the most important data structures used in de-novo genome assembly algorithms, especially for NGS data. There is a growing need for parallel data structures and algorithms due to the increasing number of cores in…
A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique…
In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On…
Orientable sequences of order n are infinite periodic sequences with symbols drawn from a finite alphabet of size k with the property that any particular subsequence of length n occurs at most once in a period in either direction. They were…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…