Related papers: Bin Packing Problem: Two Approximation Algorithms
The muffin problem asks us to divide $m$ muffins into pieces and assign each of those pieces to one of $s$ students so that the sizes of the pieces assigned to each student total $m/s$, with the objective being to maximize the size of the…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
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…
We study different online optimization problems in the random-order model. There is a finite set of bins with known capacity and a finite set of items arriving in a random order. Upon arrival of an item, its size and its value for each of…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension $N$ on a distributed computing network of $N$ nodes that is connected in a binary communication tree.…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the…
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…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
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 consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types,…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…