Related papers: Constrained Orthogonal Segment Stabbing
Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance…
We consider two problems on simplicial complexes: the Optimal Bounded Chain Problem and the Optimal Homologous Chain Problem. The Optimal Bounded Chain Problem asks to find the minimum weight $d$-chain in a simplicial complex $K$ bounded by…
Let $\mathscr O$ be a set of $n$ disjoint obstacles in $\mathbb{R}^2$, $\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\mathscr M$, respectively. Given a point $p$ in…
We consider problems of the following type: given a graph $G$, how many edges are needed in the worst case for a sparse subgraph $H$ that approximately preserves distances between a given set of node pairs $P$? Examples include pairwise…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
In this paper, we discuss the algorithm engineering aspects of an O(n^2)-time algorithm [6] for computing a minimum-area convex polygon that intersects a set of n isothetic line segments.
According to the Erd\H{o}s-Szekeres theorem, for every $n$, a sufficiently large set of points in general position in the plane contains $n$ in convex position. In this note we investigate the line version of this result, that is, we want…
The Euclidean Steiner Tree Problem (EST) seeks a minimum-cost tree interconnecting a given set of terminal points in the Euclidean plane, allowing the use of additional intersection points. In this paper, we consider two variants that…
We study the Requirement Cut problem, a generalization of numerous classical graph partitioning problems including Multicut, Multiway Cut, $k$-Cut, and Steiner Multicut among others. Given a graph with edge costs, terminal groups $(S_1,…
We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average…
The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Somewhat less well known is Erd\H{o}s' distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear…
A graph $G=(V,E)$ is a support of a hypergraph $H=(V,S)$ if every hyperedge induces a connected subgraph in $G$. Supports are used for certain types of hypergraph visualizations. In this paper we consider visualizing spatial hypergraphs,…
Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
Given an undirected graph $G$, the Densest $k$-subgraph problem (DkS) asks to compute a set $S \subset V$ of cardinality $\left\lvert S\right\rvert \leq k$ such that the weight of edges inside $S$ is maximized. This is a fundamental NP-hard…
Friedman and Linial introduced the convex body chasing problem to explore the interplay between geometry and competitive ratio in metrical task systems. In convex body chasing, at each time step $t \in \mathbb{N}$, the online algorithm…
We consider the problem of deciding, given a sequence of regions, if there is a choice of points, one for each region, such that the induced polyline is simple or weakly simple, meaning that it can touch but not cross itself. Specifically,…
We study fundamental point-line covering problems in computational geometry, in which the input is a set $S$ of points in the plane. The first is the Rich Lines problem, which asks for the set of all lines that each covers at least…
A set $S\subseteq V(G)$ of a graph $G$ is a dominating set if each vertex has a neighbor in $S$ or belongs to $S$. Let $\gamma(G)$ be the cardinality of a minimum dominating set in $G$. The bondage number $b(G)$ of a graph $G$ is the…
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds…