Related papers: When is String Reconstruction using de Bruijn Grap…
Converting a set of sequencing reads into a lossless compact data structure that encodes all the relevant biological information is a major challenge. The classical approaches are to build the string graph or the de Bruijn graph. Each has…
Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial…
The problem of graph reconstruction has been studied in its various forms over the years. In particular, the Reconstruction Conjecture, proposed by Ulam and Kelly in 1942, has attracted much research attention and yet remains one of the…
The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
A directed graph is called Eulerian, if it contains a tour that traverses every arc in the graph exactly once. We study the problem of Eulerian extension (EE) where a directed multigraph G and a weight function is given and it is asked…
The $r$-th iterated line graph $L^{r}(G)$ of a graph $G$ is defined by: (i) $L^{0}(G) = G$ and (ii) $L^{r}(G) = L(L^{(r- 1)}(G))$ for $r > 0$, where $L(G)$ denotes the line graph of $G$. The Hamiltonian Index $h(G)$ of $G$ is the smallest…
Genome assembly asks to reconstruct an unknown string from many shorter substrings of it. Even though it is one of the key problems in Bioinformatics, it is generally lacking major theoretical advances. Its hardness stems both from…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
The de Bruijn graph plays an important role in bioinformatics, especially in the context of de novo assembly. However, the representation of the de Bruijn graph in memory is a computational bottleneck for many assemblers. Recent papers…
The formal version of our work has been published in BMC Bioinformatics and can be found here: http://www.biomedcentral.com/1471-2105/13/S6/S1 Motivation: To tackle the problem of huge memory usage associated with de Bruijn graph-based…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
The Euler genus of a graph is a fundamental and well-studied parameter in graph theory and topology. Computing it has been shown to be NP-hard by [Thomassen '89 & '93], and it is known to be fixed-parameter tractable. However, the…
Graph-structured data is ubiquitous in practice and often processed using graph neural networks (GNNs). With the adoption of recent laws ensuring the ``right to be forgotten'', the problem of graph data removal has become of significant…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
Genome sequencing is essential to decode genetic information, identify organisms, understand diseases and advance personalized medicine. A critical step in any genome sequencing technique is genome assembly. However, de novo genome…
A quest to determine the complete sequence of a human DNA from telomere to telomere started three decades ago and was finally completed in 2021. This accomplishment was a result of a tremendous effort of numerous experts who engineered…
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…
We consider the following graph reconstruction problem: given an unweighted connected graph $G = (V,E)$ with visible vertex set $V$ and an oracle which takes two vertices $u,v \in V$ and returns the shortest path distance between $u$ and…