Related papers: New Lower Bounds for Reachability in Vector Additi…
We study range spaces, where the ground set consists of either polygonal curves in $\mathbb{R}^d$ or polygonal regions in the plane that may contain holes and the ranges are balls defined by an elastic distance measure, such as the…
Despite the possibility to quickly compute reachable sets of large-scale linear systems, current methods are not yet widely applied by practitioners. The main reason for this is probably that current approaches are not push-button-capable…
We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
VC-dimension and VC-density are measures of combinatorial complexity of set systems. VC-dimension was first introduced in the context of statistical learning theory, and is tightly related to the sample complexity in PAC learning.…
Weighted geometric set-cover problems arise naturally in several geometric and non-geometric settings (e.g. the breakthrough of Bansal-Pruhs (FOCS 2010) reduces a wide class of machine scheduling problems to weighted geometric set-cover).…
In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said…
If a two-player social welfare maximization problem does not admit a PTAS, we prove that any maximal-in-range truthful mechanism that runs in polynomial time cannot achieve an approximation factor better than 1/2. Moreover, for the k-player…
A basic problem in constant dimension subspace coding is to determine the maximal possible size ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in ${\bf F}_q^n$ such that the subspace distance satisfies…
Modern deep learning models capture the semantics of complex data by transforming them into high-dimensional embedding vectors. Emerging applications, such as retrieval-augmented generation, use approximate nearest neighbor (ANN) search in…
The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code…
We study the Vector Bin Packing and the Vector Bin Covering problems, multidimensional generalizations of the Bin Packing and the Bin Covering problems, respectively. In the Vector Bin Packing, we are given a set of $d$-dimensional vectors…
We study hardness of reoptimization of the fundamental and hard to approximate SetCover problem. Reoptimization considers an instance together with a solution and a modified instance where the goal is to approximate the modified instance…
In Maximum $k$-Vertex Cover (Max $k$-VC), the input is an edge-weighted graph $G$ and an integer $k$, and the goal is to find a subset $S$ of $k$ vertices that maximizes the total weight of edges covered by $S$. Here we say that an edge is…
The orthogonality dimension of a graph $G$ over $\mathbb{R}$ is the smallest integer $k$ for which one can assign a nonzero $k$-dimensional real vector to each vertex of $G$, such that every two adjacent vertices receive orthogonal vectors.…
In Statistical Learning, the Vapnik-Chervonenkis (VC) dimension is an important combinatorial property of classifiers. To our knowledge, no theoretical results yet exist for the VC dimension of edited nearest-neighbour (1NN) classifiers…
We study the reachability problem for one-counter automata in which transitions can carry disequality tests. A disequality test is a guard that prohibits a specified counter value. This reachability problem has been known to be NP-hard and…
Recently Guduru and coworkers have demonstrated with neat theory and experiments that both increase of strength and of toughness are possible in the contact of a rigid sphere with concentric single scale of waviness, against a very soft…
Finding a smallest subgraph that is k-edge-connected, or augmenting a k-edge-connected graph with a smallest subset of given candidate edges to become (k+1)-edge-connected, are among the most fundamental Network Design problems. They are…
In this paper, we consider the question of computing sparse subgraphs for any input directed graph $G=(V,E)$ on $n$ vertices and $m$ edges, that preserves reachability and/or strong connectivity structures. We show $O(n+\min\{|{\cal…