Related papers: Simulating Branching Programs with Edit Distance a…

Information distances like the Hellinger distance and the Jensen-Shannon divergence have deep roots in information theory and machine learning. They are used extensively in data analysis especially when the objects being compared are high…

It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential…

A line of work initiated by Fortnow in 1997 has proven model-independent time-space lower bounds for the $\mathsf{SAT}$ problem and related problems within the polynomial-time hierarchy. For example, for the $\mathsf{SAT}$ problem, the…

Edit distance is a fundamental measure of distance between strings and has been widely studied in computer science. While the problem of estimating edit distance has been studied extensively, the equally important question of actually…

We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…

We devise a framework for proving tight lower bounds under the counting exponential-time hypothesis #ETH introduced by Dell et al. (ACM Transactions on Algorithms, 2014). Our framework allows us to convert classical #P-hardness results for…

At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a $2^{o(k \log k)} \cdot n^{\mathcal{O}(1)}$-time algorithm on graphs of treewidth…

Partitioning a sequence of length $n$ into $k$ coherent segments (Seg) is one of the classic optimization problems. As long as the optimization criterion is additive, Seg can be solved exactly in $O(n^2k)$ time using a classic dynamic…

We show how to compute the edit distance between two strings of length n up to a factor of 2^{\~O(sqrt(log n))} in n^(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time,…

An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…

Given an $n$-vertex bipartite graph $I=(S,U,E)$, the goal of set cover problem is to find a minimum sized subset of $S$ such that every vertex in $U$ is adjacent to some vertex of this subset. It is NP-hard to approximate set cover to…

Edit distance is an important measure of string similarity. It counts the number of insertions, deletions and substitutions one has to make to a string $x$ to get a string $y$. In this paper we design an almost linear-size sketching scheme…

One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is decidable in…

Neighbour embeddings (NE) allow the representation of high dimensional datasets into lower dimensional spaces and are often used in data visualisation. In practice, accelerated approximations are employed to handle very large datasets.…

Efficiently determining the satisfiability of a boolean equation -- known as the SAT problem for brevity -- is crucial in various industrial problems. Recently, the advent of deep learning methods has introduced significant potential for…

We show improved fine-grained hardness of two key lattice problems in the $\ell_p$ norm: Bounded Distance Decoding to within an $\alpha$ factor of the minimum distance ($\mathrm{BDD}_{p, \alpha}$) and the (decisional) $\gamma$-approximate…

The Closest Vector Problem (CVP) is a computational problem in lattices that is central to modern cryptography. The study of its fine-grained complexity has gained momentum in the last few years, partly due to the upcoming deployment of…

We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…

It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer under the curse of dimensionality (COD) in the sense that…

A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…