Related papers: De Bruijn Graph Homomorphisms and Recursive De Bru…
deBruijn graphs are widely used in genomics and computer science. In this paper we present a novel approach to finding weights on edges of doubly weighted deBruijn graphs. Given any fixed set of weights on vertices, we use a repeated…
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…
A de Bruijn cycle is a cyclic listing of length A, of a collection of A combinatorial objects, so that each object appears exactly once as a set of consecutive elements in the cycle. In this paper, we show the power of de Bruijn's original…
We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.…
We present practical algorithms for generating universal cycles uniformly at random. In particular, we consider universal cycles for shorthand permutations, subsets and multiset permutations, weak orders, and orientable sequences.…
We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware graph neural network architecture for time-resolved data on dynamic graphs. Our approach accounts for temporal-topological patterns that unfold in the causal topology…
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
This paper introduces the de Bruijn graph edge minimization problem, which is related to the compression of de Bruijn graphs: find the order-k de Bruijn graph with minimum edge count among all orders. We describe an efficient algorithm that…
Motivated to find the answers to some of the questions that have occurred in recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special classes of grid graphs we started the investigation of spanning unions of cycles,…
We put forward new general criteria to design successor rules that generate binary de Bruijn sequences. Prior fast algorithms based on successor rules in the literature are then shown to be special instances. We implemented the criteria to…
Eigenvectors of the Laplacian of a cycle graph exhibit the sinusoidal characteristics of the standard DFT basis, and signals defined on such graphs are amenable to linear shift invariant (LSI) operations. In this paper we propose to reduce…
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian; this baseline result is used as the basis of existence proofs for universal cycles (also known as deBruijn cycles or $U$-cycles) of several…
Understanding how the cycles of a graph or digraph behave in general has always been an important point of graph theory. In this paper, we study the question of finding a set of $k$ vertex-disjoint cycles (resp. directed cycles) of distinct…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
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…
This paper is focused in designing an efficient on-line algorithm to reconstruct a DNA sequence and search the genes in it, we assume that the segment have no mutation or reading error, the algorithm is based on de Bruijn Graph for…
Since counting subgraphs in general graphs is, by and large, a computationally demanding problem, it is natural to try and design fast algorithms for restricted families of graphs. One such family that has been extensively studied is that…
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…
We devise constant-factor approximation algorithms for finding as many disjoint cycles as possible from a certain family of cycles in a given planar or bounded-genus graph. Here disjoint can mean vertex-disjoint or edge-disjoint, and the…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…