Related papers: Bin Packing with Multiple Colors
Consolidation of loose packages into transport units is a fundamental activity offered by logistics service-providers. Moving the transport units instead of loose packages is faster (with one movement only, multiple packages are loaded…
In this work, we present a branch-and-price algorithm to solve the weighted version of the List Coloring Problem, based on a vertex cover formulation by stable sets. This problem is interesting for its applications and also for the many…
We consider two well-known natural variants of bin packing, and show that these packing problems admit asymptotic fully polynomial time approximation schemes (AFPTAS). In bin packing problems, a set of one-dimensional items of size at most…
We survey the main formulations and solution methods for two-dimensional orthogonal cutting and packing problems, where both items and bins are rectangles. We focus on exact methods and relaxations for the four main problems from the…
Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…
In bike sharing systems the quality of the service to the users strongly depends on the strategy adopted to reposition the bikes. The bike repositioning problem is in general very complex as it involves different interrelated decisions: the…
The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…
We study range-searching for colored objects, where one has to count (approximately) the number of colors present in a query range. The problems studied mostly involve orthogonal range-searching in two and three dimensions, and the dual…
In this paper, we formulate the colorization problem into a multinomial classification problem and then apply a weighted function to classes. We propose a set of formulas to transform color values into color classes and vice versa. To…
Let $S$ be a finite set of geometric objects partitioned into classes or \emph{colors}. A subset $S'\subseteq S$ is said to be \emph{balanced} if $S'$ contains the same amount of elements of $S$ from each of the colors. We study several…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…
Two-Bar Charts Packing Problem is to pack $n$ two-bar charts (2-BCs) in a minimal number of unit-capacity bins. This problem generalizes the strongly NP-hard Bin Packing Problem. We prove that the problem remains strongly NP-hard even if…
We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion and repacking of previously packed items is allowed. The goal is, of course, to minimize both the number of bins used as well as the…
Algorithmic support systems often return optimal solutions that are hard to understand. Effective human-algorithm collaboration, however, requires interpretability. When machine solutions are equally optimal, humans must select one, but a…
We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
This paper presents a parallel genetic algorithm for three dimensional bin packing with heterogeneous bins using Hadoop Map-Reduce framework. The most common three dimensional bin packing problem which packs given set of boxes into minimum…
We describe simple linear time algorithms for coloring the squares of balanced and unbalanced quadtrees so that no two adjacent squares are given the same color. If squares sharing sides are defined as adjacent, we color balanced quadtrees…
Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition into disjoint colourings, we speak of a packing.…
We consider a Bar Charts Packing Problem (BCPP), in which it is necessary to pack bar charts (BCs) in a strip of minimum length. The problem is, on the one hand, a generalization of the Bin Packing Problem (BPP), and, on the other hand, a…