Defragmenting the Module Layout of a Partially Reconfigurable Device

Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules leads to progressive fragmentation of the available space, making defragmentation an important issue. We address this problem by propose an online and an offline component for the defragmentation of the available space. We consider defragmenting the module layout on a reconfigurable device. This corresponds to solving a two-dimensional strip packing problem. Problems of this type are NP-hard in the strong sense, and previous algorithmic results are rather limited. Based on a graph-theoretic characterization of feasible packings, we develop a method that can solve two-dimensional defragmentation instances of practical size to optimality. Our approach is validated for a set of benchmark instances.Comment: 10 pages, 11 figures, 1 table, Latex, to appear in "Engineering of Reconfigurable Systems and Algorithms" as a "Distinguished Paper

About Casting 2D-Bin Packing into Network Flow Theory

In this paper, we aim at making appear the way Flow and Multicommodity Flow Theory may be used in order to deal with combinatorial geometry problems like the 2D-Bin Packing problem. In order to do it, we introduce a notion of no circuit double flow, we state a Reformulation Theorem which ties some multicommodity flow model with a given bin-packing problem, and we provide an algorithm whose purpose is to study the way one may deal with the no circuit constraint which is at the core of our multicommodity flow

Three-Dimensional Container Loading: A Simulated Annealing Approach

High utilization of cargo volume is an essential factor in the success of modern enterprises in the market. Although mathematical models have been presented for container loading problems in the literature, there is still a lack of studies that consider practical constraints. In this paper, a Mixed Integer Linear Programming is developed for the problem of packing a subset of rectangular boxes inside a container such that the total value of the packed boxes is maximized while some realistic constraints, such as vertical stability, are considered. The packing is orthogonal, and the boxes can be freely rotated into any of the six orientations. Moreover, a sequence triple-based solution methodology is proposed, simulated annealing is used as modeling technique, and the situation where some boxes are preplaced in the container is investigated. These preplaced boxes represent potential obstacles. Numerical experiments are conducted for containers with and without obstacles. The results show that the simulated annealing approach is successful and can handle large number of packing instances

A New Quasi-Human Algorithm for Solving the Packing Problem of Unit Equilateral Triangles

The packing problem of unit equilateral triangles not only has the theoretical significance but also offers broad prospects in material processing and network resource optimization. Because this problem is nondeterministic polynomial (NP) hard and has the feature of continuity, it is necessary to limit the placements of unit equilateral triangles before optimizing and obtaining approximate solution (e.g., the unit equilateral triangles are not allowed to be rotated). This paper adopts a new quasi-human strategy to study the packing problem of unit equilateral triangles. Some new concepts are put forward such as side-clinging action, and an approximation algorithm for solving the addressed problem is designed. Time complexity analysis and the calculation results indicate that the proposed method is a polynomial time algorithm, which provides the possibility to solve the packing problem of arbitrary triangles

A New Quasi-Human Algorithm for Solving the Packing Problem of Unit Equilateral Triangles

The packing problem of unit equilateral triangles not only has the theoretical significance but also offers broad prospects in material processing and network resource optimization. Because this problem is nondeterministic polynomial (NP) hard and has the feature of continuity, it is necessary to limit the placements of unit equilateral triangles before optimizing and obtaining approximate solution (e.g., the unit equilateral triangles are not allowed to be rotated). This paper adopts a new quasi-human strategy to study the packing problem of unit equilateral triangles. Some new concepts are put forward such as side-clinging action, and an approximation algorithm for solving the addressed problem is designed. Time complexity analysis and the calculation results indicate that the proposed method is a polynomial time algorithm, which provides the possibility to solve the packing problem of arbitrary triangles

ЗАДАЧИ ДВУМЕРНОЙ ПРЯМОУГОЛЬНОЙ УПАКОВКИ И РАСКРОЯ: ОБЗОР

Приводится обзор результатов по решению задач двумерной прямоугольной упаковки и раскроя. Рассматриваются основные формулировки, математические модели и алгоритмы решения задач ортогональной упаковки прямоугольных предметов в контейнер или полубесконечную полосу и двумерного прямоугольного (в том числе гильотинного) раскроя. Основное внимание уделяется эвристическим алгоритмам и метаэвристикам (генетическим алгоритмам, поиску с запретами, метаэвристике муравьиной колонии)