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of 532
pro vyhledávání: '"van Renssen A"'
We consider the problem of computing an approximate weighted shortest path in a weighted subdivision, with weights assigned from the set $\{0, 1, \infty\}$. We present a data structure $B$, which stores a set of convex, non-overlapping regions. These
Externí odkaz:
http://arxiv.org/abs/2407.01951
Autor:
van Renssen, André
In this paper, we describe how we changed the structure of problem sessions in an algorithmic subject, in order to improve student confidence. The subject in question is taught to very large cohorts of (around 900) students, though our approach can b
Externí odkaz:
http://arxiv.org/abs/2311.12365
Given a set of $n$ point robots inside a simple polygon $P$, the task is to move the robots from their starting positions to their target positions along their shortest paths, while the mutual visibility of these robots is preserved. Previous work on
Externí odkaz:
http://arxiv.org/abs/2309.16901
Given a set of $n\geq 1$ autonomous, anonymous, indistinguishable, silent, and possibly disoriented mobile unit disk (i.e., fat) robots operating following Look-Compute-Move cycles in the Euclidean plane, we consider the Pattern Formation problem: fr
Externí odkaz:
http://arxiv.org/abs/2309.14649
We present a near-linear time approximation algorithm for the subtrajectory cluster problem of $c$-packed trajectories. The problem involves finding $m$ subtrajectories within a given trajectory $T$ such that their Fr\'echet distances are at most $(1
Externí odkaz:
http://arxiv.org/abs/2307.10610
Autor:
Buchin, Kevin, Gudmundsson, Joachim, Kalb, Antonia, Popov, Aleksandr, Rehs, Carolin, van Renssen, André, Wong, Sampson
Given a point set $P$ in the Euclidean plane and a parameter $t$, we define an \emph{oriented $t$-spanner} $G$ as an oriented subgraph of the complete bi-directed graph such that for every pair of points, the shortest closed walk in $G$ through those
Externí odkaz:
http://arxiv.org/abs/2306.17097
Given a set of $n\geq 1$ unit disk robots in the Euclidean plane, we consider the Pattern Formation problem, i.e., the robots must reposition themselves to form a given target pattern. This problem arises under obstructed visibility, where a robot ca
Externí odkaz:
http://arxiv.org/abs/2306.14440
Spanner construction is a well-studied problem and Delaunay triangulations are among the most popular spanners. Tight bounds are known if the Delaunay triangulation is constructed using an equilateral triangle, a square, or a regular hexagon. However
Externí odkaz:
http://arxiv.org/abs/2211.11987
Given a set of $n \geq 1$ unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This problem
Externí odkaz:
http://arxiv.org/abs/2206.14423
Autor:
Lee, Keenan, van Renssen, André
We present sweeping line graphs, a generalization of $\Theta$-graphs. We show that these graphs are spanners of the complete graph, as well as of the visibility graph when line segment constraints or polygonal obstacles are considered. Our proofs use
Externí odkaz:
http://arxiv.org/abs/2109.05689