We consider a game-theoretic bin packing problem and we study the convergence time to a Nash equilibrium. We show that, if the best-response strategy is used, then the number of steps needed to reach Nash equilibrium is O(mw2 max + nwmax) and O(nkwmax), where n, m, k and wmax denotes, resp., the number of items, the number of bins, the number of distinct item sizes, and the size of a largest item.

The effect of vacuum packing on the shelf-life of sausages produced from Capoeta umbla were investigated during storage periods. For this purpose, microbial, chemical and sensory changes were analyzed throughout the storage time. The microbial flora of the sausages comprised mainly mesophilic bacteria, psychrotrophic bacteria, lactic acid bacteria, yeast and molds. Escherichia coli, Staphylcocc...

The effect of vacuum packing on the shelf-life of sausages produced from Capoeta umbla were investigated during storage periods. For this purpose, microbial, chemical and sensory changes were analyzed throughout the storage time. The microbial flora of the sausages comprised mainly mesophilic bacteria, psychrotrophic bacteria, lactic acid bacteria, yeast and molds. Escherichia coli, Staphylcocc...

We introduce an orthoplicial Apollonian sphere packing, which is a sphere packing obtained by successively inverting a configuration of 8 spheres with 4-orthplicial tangency graph. We will show that there are such packings in which the bends of all constituent spheres are integral, and establish the asymptotic local-global principle for the set of bends in these packings.

The rectangle packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our algorithm picks the x-coordinates of all the rectangles before picking any of the y-coordinates. For the x-coordinates, we present a dynamic variable ordering heuristic and an adaptation of a pruning algorithm used in previous solvers. We then...

We study online interval coloring problems with bandwidth. We are interested in some variants motivated by bin packing problems. Specifically we consider open-end coloring, cardinality constrained coloring, coloring with vector constraints and finally a combination of both the cardinality and the vector constraints. We construct competitive algorithms for each of the variants. Additionally, we ...

We consider a game-theoretic bin packing problem with identical items, and we study the convergence time to a Nash equilibrium. In the model proposed, users choose their strategy simultaneously. We deal with two bins and multiple bins cases. We consider the case when users know the load of all bins and cases with less information. We consider two approaches, depending if the system can undo mov...

Edmonds’ fundamental theorem on arborescences [4] characterizes the existence of k pairwise edge-disjoint arborescences with the same root in a directed graph. In [9], Lovász gave an elegant alternative proof which became the base of many extensions of Edmonds’ result. In this paper, we use a modification of Lovász’ method to prove a theorem on covering intersecting bi-set families under matroi...

We prove a tight lower bound on the asymptotic performance ratio ρ of the bounded space online d-hypercube bin packing problem, solving an open question raised in 2005. In the classic d-hypercube bin packing problem, we are given a sequence of d-dimensional hypercubes and we have an unlimited number of bins, each of which is a d-dimensional unit hypercube. The goal is to pack (orthogonally) the...

We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity then we present a 6 5 -approximation algorithm for a sp...