Groupe

GT

Seminars are given every Friday from 2:00 to 3:00 (usually in room 178, but not for the time being). You are welcome 10 minutes earlier for tea, coffee and cake.

In order to receive the announcements, just send an email to sympa@diff.u-bordeaux.fr with subject "subscribe labri.go-gt Cookie Monster", where Cookie is your first name and Monster your last name.

See the agenda of the seminars: webmel.u-bordeaux.fr/service/user/bf-labri.go@u-bordeaux.fr/gt.html https://webmel.u-bordeaux.fr/home/bf-labri.ca@u-bordeaux.fr/gt.go.html; to add it to yours webmel.u-bordeaux.fr/service/user/bf-labri.go@u-bordeaux.fr/gt.ics https://webmel.u-bordeaux.fr/home/bf-labri.ca@u-bordeaux.fr/gt.go.ics , or flash the following QRCode:

Next talks:

The online talks are available here : https://webconf.u-bordeaux.fr/b/mar-ef4-zed.

Vendredi 21 Juin 14h - Nicolas Bonichon
Freeze-Tag in $L_1$ has Wake-up Time Five with Linear Complexity
The Freeze-Tag Problem, introduced in Arkin et al. (SODA'02) consists of waking up a swarm of n robots, starting from a single active robot. In the basic geometric version, every robot is given coordinates in the plane. As soon as a robot is awakened, it can move towards inactive robots to wake them up. The goal is to minimize the makespan of the last robot, the makespan.

Despite significant progress on the computational complexity of this problem and on approximation algorithms, the characterization of exact bounds on the makespan remains one of the main open questions. In this paper, we settle this question for the $\ell_1$-norm, showing that a makespan of at most 5r can always be achieved, where r is the maximum distance between the initial active robot and any sleeping robot. Moreover, a schedule achieving a makespan of at most 5r can be computed in time O(n). Both bounds, the time and the makespan are optimal. Our results also imply for the $\ell_2$-norm a new upper bound of 5√2r ≈ 7.07r on the makespan, improving the best known bound of (5+2√2+√5)r ≈ 10.06r.

Along the way, we introduce new linear time wake-up strategies, that apply to any norm and show that an optimal bound on the makespan can always be achieved by a schedule computable in linear time.

Jobs

Group

GT Graphs and Optimization

History

 Previous Years

edit SideBar

Blix theme adapted by David Gilbert, powered by PmWiki