Related papers: Optimal Construction of Hierarchical Overlap Graph…
Reducing the cost of sequencing genomes provided by next-generation sequencing technologies has greatly increased the number of genomic projects. As a result, there is a growing need for better assembly and assembly validation methods. One…
Given two convex polygons $P$ and $Q$ with $n$ and $m$ edges, the maximum overlap problem is to find a translation of $P$ that maximizes the area of its intersection with $Q$. We give the first randomized algorithm for this problem with…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
In the zero-error Slepian-Wolf source coding problem, the optimal rate is given by the complementary graph entropy $\overline{H}$ of the characteristic graph. It has no single-letter formula, except for perfect graphs, for the pentagon…
Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…
Massively parallel DNA sequencing technologies are revolutionizing genomics research. Billions of short reads generated at low costs can be assembled for reconstructing the whole genomes. Unfortunately, the large memory footprint of the…
We study algorithmic and structural aspects of connectivity in hypergraphs. Given a hypergraph $H=(V,E)$ with $n = |V|$, $m = |E|$ and $p = \sum_{e \in E} |e|$ the best known algorithm to compute a global minimum cut in $H$ runs in time…
An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements…
Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for…
We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…
We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the n^(log_p n + O(1)) generator-enumeration algorithm. In previous work…
The problem of Subgraph Isomorphism is defined as follows: Given a pattern H and a host graph G on n vertices, does G contain a subgraph that is isomorphic to H? Eppstein [SODA 95, J'GAA 99] gives the first linear time algorithm for…
We show that the existence of a homomorphism from an $n$-vertex graph $G$ to an $h$-vertex graph $H$ can be decided in time $2^{O(n)}h^{O(1)}$ and polynomial space if $H$ comes from a family of graphs that excludes a topological minor. The…
Recently, Marcus et al. (Bioinformatics 2014) proposed to use a compressed de Bruijn graph to describe the relationship between the genomes of many individuals/strains of the same or closely related species. They devised an $O(n \log g)$…
The Sparsest Cut is a fundamental optimization problem that has been extensively studied. For planar inputs the problem is in $P$ and can be solved in $\tilde{O}(n^3)$ time if all vertex weights are $1$. Despite a significant amount of…
De novo genome assembly is challenging in highly repetitive regions; however, reference-guided assemblers often suffer from bias. We propose a framework for pangenome-guided sequence assembly, which can resolve short-read data in complex…