Related papers: General uncrossing covering paths inside the axis-…
For $S\subseteq V(G)$ and $|S|\geq 2$, $\lambda(S)$ is the maximum number of edge-disjoint trees connecting $S$ in $G$. For an integer $k$ with $2\leq k\leq n$, the \emph{generalized $k$-edge-connectivity} $\lambda_k(G)$ of $G$ is then…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{\textrm{th}}$ item has width $w(i)$, height $h(i)$, and…
The matroid intersection problem is a fundamental problem that has been extensively studied for half a century. In the classic version of this problem, we are given two matroids $\mathcal{M}_1 = (V, \mathcal{I}_1)$ and $\mathcal{M}_2 = (V,…
We design an algorithm for control of a linear switched system by means of Geometric Algebra. More precisely, we develop a switching path searching algorithm for a two-dimensional linear dynamical switched system with non-singular matrix…
Consider a robot that remembers only the starting position and walks along a knot once on a knot diagram, switching every undercrossing it meets until it returns to the starting position. We observe that the robot produces an ascending…
In Part I of this article we generalize the Linearized Doubling (LD) approach, introduced in earlier work by NK, by proving a general theorem stating that if $\Sigma$ is a closed minimal surface embedded in a Riemannian three-manifold…
The crossing number is the smallest number of pairwise edge-crossings when drawing a graph into the plane. There are only very few graph classes for which the exact crossing number is known or for which there at least exist constant…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
An axis-parallel $b$-dimensional box is a Cartesian product $R_1\times R_2\times...\times R_b$ where $R_i$ is a closed interval of the form $[a_i,b_i]$ on the real line. For a graph $G$, its \emph{boxicity} box(G) is the minimum dimension…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…
A {\it path covering} of a graph $G$ is a set of vertex disjoint paths of $G$ containing all the vertices of $G$. The {\it path covering number} of $G$, denoted by $P(G)$, is the minimum number of paths in a path covering of $G$. An {\sl…
We present a linear programming based algorithm for computing a spanning tree $T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is $O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any spanning…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
Confluence is a novel non-Intersection over Union (IoU) alternative to Non-Maxima Suppression (NMS) in bounding box post-processing in object detection. It overcomes the inherent limitations of IoU-based NMS variants to provide a more…
In this paper, we present a new framework that exploits combinatorial optimization for efficiently generating a large variety of combinatorial objects based on graphs, matroids, posets and polytopes. Our method relies on a simple and…
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs…
A covering path for a planar point set is a path drawn in the plane with straight-line edges such that every point lies at a vertex or on an edge of the path. A covering tree is defined analogously. Let $\pi(n)$ be the minimum number such…
We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to…
Let $G$ be a graph with no isolated vertex. A matching in $G$ is a set of edges that are pairwise not adjacent in $G$, while the matching number, $\alpha'(G)$, of $G$ is the maximum size of a matching in $G$. The path covering number,…