Related papers: Comparing several heuristics for a packing problem
Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum…
An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation…
In the Two-dimensional Bin Packing (2BP) problem, we are given a set of rectangles of height and width at most one and our goal is to find an axis-aligned nonoverlapping packing of these rectangles into the minimum number of unit square…
The lack of diversity in a genetic algorithm's population may lead to a bad performance of the genetic operators since there is not an equilibrium between exploration and exploitation. In those cases, genetic algorithms present a fast and…
We consider a memory allocation problem that can be modeled as a version of bin packing where items may be split, but each bin may contain at most two (parts of) items. A 3/2-approximation algorithm and an NP-hardness proof for this problem…
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 study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack.…
The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to…
We study the classic Bin Packing problem in a fully-dynamic setting, where new items can arrive and old items may depart. We want algorithms with low asymptotic competitive ratio \emph{while repacking items sparingly} between updates.…
With the increasing size of datasets and demand for real time response for interactive applications, improving runtime for algorithms with excessive computational requirements has become increasingly important. Many different algorithms…
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
We consider a variant of the classical Bin Packing Problem, called Fully Dynamic Bin Packing. In this variant, items of a size in $(0,1]$ must be packed in bins of unit size. In each time step, an item either arrives or departs from the…
In the recent paper \cite{BDT10} we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a "good and fast" packing or…
We continue the study of two recently introduced bin packing type problems, called bin packing with clustering, and online bin packing with delays. A bin packing input consists of items of sizes not larger than 1, and the goal is to…
We explore approximation algorithms for the $d$-dimensional geometric bin packing problem ($d$BP). Caprara (MOR 2008) gave a harmonic-based algorithm for $d$BP having an asymptotic approximation ratio (AAR) of $T_{\infty}^{d-1}$ (where…
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in $(0,1]$, and a partition matroid over the items. The goal is to pack all items in a minimum number of unit-size bins, such that…
Packing is a classical problem where one is given a set of subsets of Euclidean space called objects, and the goal is to find a maximum size subset of objects that are pairwise non-intersecting. The problem is also known as the Independent…
We analyze a recently introduced concept, called the price of clustering, for variants of bin packing called open-end bin packing problems (OEBP). Input items have sizes, and they also belong to a certain number of types. The new concept…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…