Related papers: New Lower Bounds for Reachability in Vector Additi…
We study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack.…
Filtered approximate nearest neighbor search (FANNS), an extension of approximate nearest neighbor search (ANNS) that incorporates scalar filters, has been widely applied to constrained retrieval of vector data. Despite its growing…
The VC-dimension, introduced by Vapnik and Chervonenkis in 1968 in the context of learning theory, has in recent years provided a rich source of problems in combinatorial geometry. Given $E\subseteq \mathbb{F}_q^d$ or $E\subseteq…
We study a core algorithmic problem in network design called ${F}$-augmentation that involves increasing the connectivity of a given family of cuts ${F}$. Over 30 years ago, Williamson et al. (STOC `93) provided a 2-approximation…
A recent breakthrough by K\"unnemann, Mazowiecki, Sch\"utze, Sinclair-Banks, and Wegrzycki (ICALP, 2023) bounds the running time for the coverability problem in $d$-dimensional vector addition systems under unary encoding to $n^{2^{O(d)}}$,…
A classical open problem in combinatorial geometry is to obtain tight asymptotic bounds on the maximum number of k-level vertices in an arrangement of n hyperplanes in d dimensions (vertices with exactly k of the hyperplanes passing below…
The NP-hard Metric Dimension problem is to decide for a given graph G and a positive integer k whether there is a vertex subset of size at most k that separates all vertex pairs in G. Herein, a vertex v separates a pair {u,w} if the…
Approximate nearest neighbor search (ANNS) is a fundamental problem in vector databases and AI infrastructures. Recent graph-based ANNS algorithms have achieved high search accuracy with practical efficiency. Despite the advancements, these…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…
We consider numerical functions weakly computable by grammar-controlled vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can weakly compute all fast growing functions $F_\alpha$ for $\alpha<\omega^\omega$, hence…
A new framework for solving the hierarchy problem was recently proposed which does not rely on low energy supersymmetry or technicolor. The fundamental Planck mass is at a $\tev$ and the observed weakness of gravity at long distances is due…
We consider the Connectivity Augmentation Problem (CAP), a classical problem in the area of Survivable Network Design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a…
Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and…
Approximate Nearest Neighbor Search (ANNS) on high-dimensional vectors has become a fundamental and essential component in various machine learning tasks. Recently, with the rapid development of deep learning models and the applications of…
The Weighted Tree Augmentation Problem (WTAP) is a fundamental well-studied problem in the field of network design. Given an undirected tree $G=(V,E)$, an additional set of edges $L \subseteq V\times V$ disjoint from $E$ called…
We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that…
We show by reduction from the Orthogonal Vectors problem that algorithms with strongly subquadratic running time cannot approximate the Fr\'echet distance between curves better than a factor $3$ unless SETH fails. We show that similar…
We consider pushdown systems that store, instead of a single word, a Mazurkiewicz trace on its stack. These systems are special cases of valence automata over graph monoids and subsume multi-stack systems. We identify a class of such…