Related papers: Constrained de Bruijn Codes: Properties, Enumerati…
Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…
For positive integers $k,n$, a de Bruijn sequence $B(k,n)$ is a finite sequence of elements drawn from $k$ characters whose subwords of length $n$ are exactly the $k^n$ words of length $n$ on $k$ characters. This paper introduces the…
The reduction of the fragment assembly problem to (variations of) the classical Eulerian trail problem [Pevzner et al., PNAS 2001] has led to remarkable progress in genome assembly. This reduction employs the notion of de Bruijn graph…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
In this article, we show how to transform a colored de Bruijn graph (dBG) into a practical index for processing massive sets of sequencing reads. Similar to previous works, we encode an instance of a colored dBG of the set using BOSS and a…
We generalize the notion of a de Bruijn sequence to a "multi de Bruijn sequence": a cyclic or linear sequence that contains every k-mer over an alphabet of size q exactly m times. For example, over the binary alphabet {0,1}, the cyclic…
Machine learning models are widely used for real-world applications, such as document analysis and vision. Constrained machine learning problems are problems where learned models have to both be accurate and respect constraints. For…
While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…
Universal cycles, such as De Bruijn cycles, are cyclic sequences of symbols that represent every combinatorial object from some family exactly once as a consecutive subsequence. Graph universal cycles are a graph analogue of universal…
Every binary De~Bruijn sequence of order n satisfies a recursion 0=x_n+x_0+g(x_{n-1}, ..., x_1). Given a function f on (n-1) bits, let N(f; r) be the number of functions generating a De Bruijn sequence of order n which are obtained by…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
Transformer architectures have been successfully used in learning source code representations. The fusion between a graph representation like Abstract Syntax Tree (AST) and a source code sequence makes the use of current approaches…
In various wireless systems, such as sensor RFID networks and body area networks with implantable devices, the transmitted signals are simultaneously used both for information transmission and for energy transfer. In order to satisfy the…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…
Experimental results show that, when the order $n$ is odd, there are de Bruijn sequences such that the corresponding complement sequence and the reverse sequence are the same. In this paper, we propose one efficient method to generate such…
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on…
The rapid expansion of genomic sequence data calls for new methods to achieve robust sequence representations. Existing techniques often neglect intricate structural details, emphasizing mainly contextual information. To address this, we…
Graph constraint logic is a framework introduced by Hearn and Demaine, which provides several problems that are often a convenient starting point for reductions. We study the parameterized complexity of Constraint Graph Satisfiability and…