Tootfinder

Morgen dus waarschijnlijk de hele dag een van de debatten die de meeste aandacht zal krijgen, maar inhoudelijk totaal niets waard hoogst waarschijnlijk.
@… #politiek #debat

'Regeling van werkzaamheden' die voor de hele namiddag en avond ingepland is.
Ik heb het altijd al een best grappige omschrijving gevonden voor dit soort debatten. 😉
@…
#Politiek #debat

A first view on the density of 5-planar graphs
Aaron B\"ungener, Jakob Franz, Michael Kaufmann, Maximilian Pfister
https://arxiv.org/abs/2505.24364 ht…

A first view on the density of 5-planar graphs
$k$-planar graphs are generalizations of planar graphs that can be drawn in the plane with at most $k > 0$ crossings per edge. One of the central research questions of $k$-planarity is the maximum edge density, i.e., the maximum number of edges a $k$-planar graph on $n$ vertices may have. While there are numerous results for the classes of general $k$-planar graphs for $k\leq 2$, there are only very few results for increasing $k=3$ or $4$ due to the complexity of the classes. We make a first st…

(YouTube playlist) Some 15 years after receiving his Dobelle brain implant for restoring vision, Jens ("Patient Alpha") tried The vOICe vision BCI https://www.youtube.com/playlist?list=PLmrvukzbS44SMVxMLRpd-_iTpy_Cj5liB Will Neuralink Blinds…

Approximate Light Spanners in Planar Graphs
Hung Le, Shay Solomon, Cuong Than, Csaba D. T\'oth, Tianyi Zhang
https://arxiv.org/abs/2505.24825 https://

Approximate Light Spanners in Planar Graphs
In their seminal paper, Althöfer et al. (DCG 1993) introduced the {\em greedy spanner} and showed that, for any weighted planar graph $G$, the weight of the greedy $(1+ε)$-spanner is at most $(1+\frac{2}ε) \cdot w(MST(G))$, where $w(MST(G))$ is the weight of a minimum spanning tree $MST(G)$ of $G$. This bound is optimal in an {\em existential sense}: there exist planar graphs $G$ for which any $(1+ε)$-spanner has a weight of at least $(1+\frac{2}ε) \cdot w(MST(G))$. However, as an {\em a…

The minimum size of maximal bipartite IC-plane graphs with given connectivity
Guiping Wang, Yuanqiu Huang, Zhangdong Ouyang, Licheng Zhang
https://arxiv.org/abs/2506.00878

The minimum size of maximal bipartite IC-plane graphs with given connectivity
Recently, the problem of establishing bounds on the edge density of 1-planar graphs, including their subclass IC-planar graphs, has received considerable attention. In 2018, Angelini et al. showed that any n-vertex bipartite IC-planar graph has at most 2.25n-4 edges, which implies that bipartite IC-planar graphs have vertex-connectivity at most 4. In this paper, we prove that any n-vertex maximal bipartite IC-plane graph with connectivity 2 has at least 3/2n-2 edges, and those with connectivity…

Haptic Rapidly-Exploring Random Trees: A Sampling-based Planner for Quasi-static Manipulation Tasks
Lin Yang, Huu-Thiet Nguyen, Donghan Yu, Chen Lv, Domenico Campolo
https://arxiv.org/abs/2506.00351

Haptic Rapidly-Exploring Random Trees: A Sampling-based Planner for Quasi-static Manipulation Tasks
In this work, we explore how conventional motion planning algorithms can be reapplied to contact-rich manipulation tasks. Rather than focusing solely on efficiency, we investigate how manipulation aspects can be recast in terms of conventional motion-planning algorithms. Conventional motion planners, such as Rapidly-Exploring Random Trees (RRT), typically compute collision-free paths in configuration space. However, in manipulation tasks, intentional contact is often necessary. For example, whe…

Exploiting Euclidean Distance Field Properties for Fast and Safe 3D planning with a modified Lazy Theta*
Jose A. Cobano, L. Merino, F. Caballero
https://arxiv.org/abs/2505.24024

Exploiting Euclidean Distance Field Properties for Fast and Safe 3D planning with a modified Lazy Theta*
Graph search planners have been widely used for 3D path planning in the literature, and Euclidean Distance Fields (EDFs) are increasingly being used as a representation of the environment. However, to the best of our knowledge, the integration of EDFs into heuristic planning has been carried out in a loosely coupled fashion, dismissing EDF properties that can be used to accelerate/improve the planning process and enhance the safety margins of the resultant trajectories. This paper presents a fa…

Using Diffusion Ensembles to Estimate Uncertainty for End-to-End Autonomous Driving
Florian Wintel, Sigmund H. H{\o}eg, Gabriel Kiss, Frank Lindseth
https://arxiv.org/abs/2506.00560

Using Diffusion Ensembles to Estimate Uncertainty for End-to-End Autonomous Driving
End-to-end planning systems for autonomous driving are improving rapidly, especially in closed-loop simulation environments like CARLA. Many such driving systems either do not consider uncertainty as part of the plan itself, or obtain it by using specialized representations that do not generalize. In this paper, we propose EnDfuser, an end-to-end driving system that uses a diffusion model as the trajectory planner. EnDfuser effectively leverages complex perception information like fused camera …

On the maximum number of edges of outer k-planar graphs
Maximilian Pfister
https://arxiv.org/abs/2505.24490 https://arxiv.org/pdf/250…

On the maximum number of edges of outer k-planar graphs
We study the maximum number of straight-line segments connecting $n$ points in convex position in the plane, so that each segment intersects at most $k$ others. This question can also be framed as the maximum number of edges of an outer $k$-planar graph on $n$ vertices. We outline several approaches to tackle the problem with the best approach yielding an upper bound of $(\sqrt{2}+\varepsilon)\sqrt{k}n$ edges (with $\varepsilon \rightarrow 0$ for sufficiently large $k$). We further investigate …