The greedy Prefer-same de Bruijn sequence construction was first presented by Eldert, Gray, Gurk, and Rubinoff in 1958. As a greedy algorithm, it has one major downside: it requires an exponential amount of space to store the length \(2^{n}\) de Bruijn ...
In the Directed Steiner Tree (DST) problem, we are given a directed graph \(G=(V,E)\) on \(n\) vertices with edge-costs \(c\in{\mathbb{R}}_{\geq 0}^{E}\), a root vertex \(r\in V\), and a set \(K\subseteq V\setminus\{r\}\) of \(k\) terminals. ...
A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We consider sampling problems coming from Gibbs distributions, which are families of ...
It was conjectured by Gupta et al. that every planar graph can be embedded into \(\ell_{1}\) with constant distortion. However, given an \(n\)-vertex weighted planar graph, the best upper bound on the distortion is only \(O(\sqrt{\log n})\), by Rao. ...
In this article, we study the online Euclidean spanners problem for points in \(\mathbb{R}^{d}\). Given a set \(S\) of \(n\) points in \(\mathbb{R}^{d}\), a \(t\)-spanner on \(S\) is a subgraph of the underlying complete graph \(\(G=(S,\binom{S}...\)
A map is a \(2\)-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. An automorphism of a map can be thought of as a permutation of the vertices, which preserves the vertex-...
We study the identity testing problem for high-dimensional distributions. Given as input an explicit distribution \(\mu\), an \(\varepsilon \gt 0\), and access to sampling oracle(s) for a hidden distribution \(\pi\), the goal in identity testing is ...
We study the complexity of approximating the number of answers to a small query \(\varphi\) in a large database \(\mathcal{D}\). We establish an exhaustive classification into tractable and intractable cases if \(\varphi\) is a conjunctive query ...
We present an algorithm that finds a maximum cardinality \(f\)-matching of a simple graph in time \(O(n^{2/3}m)\). Here, \(f:V\to\mathbb{N}\) is a given function and an \(f\)-matching is a subgraph wherein each vertex \(v\in V\) has degree \(\(\...\)
The \(k\)-Strong Conflict-Free (\(k\)-SCF colouring problem seeks to find a colouring of the vertices of a hypergraph \(H\) using minimum number of colours so that in every hyperedge \(e\) of \(H\), there are at least \(\min\{|e|,k\}\) ...
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this significant problem in the fully dynamic setting, where elements can be both ...
We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern \(P[1\mathinner{.. }m]\) on a large repetitive text collection \(T[1\mathinner{.. }n]\) over an alphabet of size \(\sigma\), which is represented as a (...
An elimination tree for a connected graph \(G\) is a rooted tree on the vertices of \(G\) obtained by choosing a root \(x\) and recursing on the connected components of \(G-x\) to produce the subtrees of \(x\). Elimination trees appear in many ...
