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

Optimization Modulo Theories with Linear Rational Costs

In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, little work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any previous work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality. In the work described in this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of linear rational cost functions, combining SMT with standard minimization techniques. We have implemented the procedures within the MathSAT SMT solver. Due to the absence of competitors in the AR, FV and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic, currently under revision. arXiv admin note: text overlap with arXiv:1202.140

A SAT encoding for Multi-dimensional Packing Problems

International audienceThe Orthogonal Packing Problem (OPP) consists in determining if a set of items can be packed into a given container. This decision problem is NP-complete. S. P. Fekete et al. modelled the problem in which the overlaps between the objects in each dimension are represented by interval graphs. In this paper we propose a SAT encoding of Fekete et al. characterization. Some results are presented, and the efficiency of this approach is compared with other SAT encodings

A simulation-based algorithm for solving the resource-assignment problem in satellite telecommunication networks

This paper proposes an heuristic for the scheduling of capacity requests and the periodic assignment of radio resources in geostationary (GEO) satellite networks with star topology, using the Demand Assigned Multiple Access (DAMA) protocol in the link layer, and Multi-Frequency Time Division Multiple Access (MF-TDMA) and Adaptive Coding and Modulation (ACM) in the physical layer.En este trabajo se propone una heurística para la programación de las solicitudes de capacidad y la asignación periódica de los recursos de radio en las redes de satélites geoestacionarios (GEO) con topología en estrella, con la demanda de acceso múltiple de asignación (DAMA) de protocolo en la capa de enlace, y el Multi-Frequency Time Division (Acceso múltiple por MF-TDMA) y codificación y modulación Adaptable (ACM) en la capa física.En aquest treball es proposa una heurística per a la programació de les sol·licituds de capacitat i l'assignació periòdica dels recursos de ràdio en les xarxes de satèl·lits geoestacionaris (GEO) amb topologia en estrella, amb la demanda d'accés múltiple d'assignació (DAMA) de protocol en la capa d'enllaç, i el Multi-Frequency Time Division (Accés múltiple per MF-TDMA) i codificació i modulació Adaptable (ACM) a la capa física

Automating the packing heuristic design process with genetic programming

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains

Optimization in SMT with LA(Q) Cost Functions

In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, very few work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality. In this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of LA(Q) cost functions, combining SMT with standard minimization techniques. We have implemented the proposed approach within the MathSAT SMT solver. Due to the lack of competitors in AR and SMT domains, we experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach.Comment: A shorter version is currently under submissio

Optimization Models and Algorithms for Spatial Scheduling

Spatial scheduling problems involve scheduling a set of activities or jobs that each require a certain amount of physical space in order to be carried out. In these problems space is a limited resource, and the job locations, orientations, and start times must be simultaneously determined. As a result, spatial scheduling problems are a particularly difficult class of scheduling problems. These problems are commonly encountered in diverse industries including shipbuilding, aircraft assembly, and supply chain management. Despite its importance, there is a relatively scarce amount of research in the area of spatial scheduling. In this dissertation, spatial scheduling problems are studied from a mathematical and algorithmic perspective. Optimization models based on integer programming are developed for several classes of spatial scheduling problems. While the majority of these models address problems having an objective of minimizing total tardiness, the models are shown to contain a core set of constraints that are common to most spatial scheduling problems. As a result, these constraints form the basis of the models given in this dissertation and many other spatial scheduling problems with different objectives as well. The complexity of these models is shown to be at least NP-complete, and spatial scheduling problems in general are shown to be NP-hard. A lower bound for the total tardiness objective is shown, and a polynomial-time algorithm for computing this lower bound is given. The computational complexity inherent to spatial scheduling generally prevents the use of optimization models to find solutions to larger, realistic problems in a reasonable time. Accordingly, two classes of approximation algorithms were developed: greedy heuristics for finding fast, feasible solutions; and hybrid meta-heuristic algorithms to search for near-optimal solutions. A flexible hybrid algorithm framework was developed, and a number of hybrid algorithms were devised from this framework that employ local search and several varieties of simulated annealing. Extensive computational experiments showed these hybrid meta-heuristic algorithms to be effective in finding high-quality solutions over a wide variety of problems. Hybrid algorithms based on local search generally provided both the best-quality solutions and the greatest consistency

Un codage SAT pour les problèmes de placement

National audienceLe problème de placement orthogonal (OPP) consiste à déterminer si un ensemble d'objets peut etre placé dans un conteneur de taille connue. Ce problème est NP-complet. Une modélisation de ce problème à base de graphes d'intervalles a été proposée par S. P. Fekete et al. Cette modélisation permet de représenter des classes de placements équivalents, diminuant d'autant l'espace de recherche. Dans cet article nous proposons de représenter par des formules de la logique propositionnelle la modélisation de S. P. Fekete et al. Nous avons implémenté cette approche en utilisant le solveur MiniSat, et nous l'avons comparée d'une part avec les résultats de S. P. Fekete et al. sur des problèmes classiques, et d'autre part avec l'approche de T. Soh et al. basée aussi sur un codage SAT sur des problèmes de Strip Packing