Bounded space on-line variable-sized bin packing

In this paper we consider the fc-bounded space on-line bin packing problem. Some efficient approximation algorithms are described and analyzed. Selecting either the smallest or the largest available bin size to start a new bin as items arrive turns out to yield a worst-case performance bound of 2. By packing large items into appropriate bins, an efficient approximation algorithm is derived from fc-bounded space on-line bin packing algorithms and its worst-case performance bounds is 1.7 for k > 3

A Best Cost-Sharing Rule for Selfish Bin Packing

In selfish bin packing, each item is regarded as a player, who aims to minimize the cost-share by choosing a bin it can fit in. To have a least number of bins used, cost-sharing rules play an important role. The currently best known cost sharing rule has a lower bound on $PoA$ larger than 1.45, while a general lower bound 4/3 on $PoA$ applies to any cost-sharing rule under which no items have incentive unilaterally moving to an empty bin. In this paper, we propose a novel and simple rule with a $PoA$ matching the lower bound, thus completely resolving this game. The new rule always admits a Nash equilibrium and its $PoS$ is one. Furthermore, the well-known bin packing algorithm $BFD$ (Best-Fit Decreasing) is shown to achieve a strong equilibrium, implying that a stable packing with an asymptotic approximation ratio of $11/9$ can be produced in polynomial time

La symbiose entre l’homme et la nature chez François Cheng

Dans cet article, nous nous emploierons à éclaircir la relation entre l’homme et la nature dans les traductions de François Cheng, académicien d’origine chinoise. Auteur de L’Écriture poétique chinoise, suivie d’une anthologie des poèmes des Tang (1977), il a traduit dans ce recueil 87 poèmes des Tang, ainsi que les théories picturales chinoises regroupées dans son livre intitulé Souffle-Esprit. Textes théoriques chinois sur l’art pictural. Ses traductions transmettent la vision du monde des ..

On optimality of exact and approximation algorithms for scheduling problems

We consider the classical scheduling problem on parallel identical machines to minimize the makespan. Under the exponential time hypothesis (ETH), lower bounds on the running times of exact and approximation algorithms are characterized