Tootfinder

A polynomial bound on the pathwidth of graphs edge-coverable by $k$ shortest paths
Julien Baste, Lucas De Meyer, Ugo Giocanti, Etienne Objois, Timoth\'e Picavet
https://arxiv.org/abs/2510.02901

A polynomial bound on the pathwidth of graphs edge-coverable by $k$ shortest paths
Dumas, Foucaud, Perez and Todinca (2024) recently proved that every graph whose edges can be covered by $k$ shortest paths has pathwidth at most $O(3^k)$. In this paper, we improve this upper bound on the pathwidth to a polynomial one; namely, we show that every graph whose edge set can be covered by $k$ shortest paths has pathwidth $O(k^4)$, answering a question from the same paper. Moreover, we prove that when $k\leq 3$, every such graph has pathwidth at most $k$ (and this bound is tight). Fi…

I decided to be properly cyberpunk, my bar for Neotropolis needs exhaust fans on the outside. To be cinematic, the fan should turn pointlessly slow.
I bought a fan with a speed controller. It seem to use 5V PWM. Sending my own PWM, ~8% is the lowest speed. Below that it shuts off. But I want slower still.
I'm surprised this isn't a brushed DC motor or universal motor - it uses a BLDC motor.
I suspect the easiest route will be replacing with a

Approximating Multiple-Depot Capacitated Vehicle Routing via LP Rounding
Zachary Friggstad, Tobias M\"omke
https://arxiv.org/abs/2510.05321 https://ar…

Approximating Multiple-Depot Capacitated Vehicle Routing via LP Rounding
In Capacitated Vehicle Routing with Multiple Depots (CVRP-MD) we are given a set of client locations $C$ and a set of depots $R$ located in a metric space with costs $c(i,j)$ between $u,v \in C \cup R$. Additionally, we are given a capacity bound $k$. The goal is to find a collection of tours of minimum total cost such that each tour starts and ends at some depot $r \in R$ and includes at most $k$ clients and such that each client lies on at least one tour. Our main result is a $3.9365$-approxi…