Vincent Poirriez

Unbounded knapsack problem: Dynamic programming revisited

Abstract We present EDUK, an efficient dynamic programming algorithm for the unbounded knapsack problem. It is based primarily on a new and useful dominance relation, called threshold dominance , which is a strict generalization of all the previously known dominance relations. We show that combining it with a sparse representation of the iteration domain and the periodicity property leads to a drastic reduction of the solution space. We present computational experiments with various data instances to validate our ideas and demonstrate the efficiency of EDUK vis-a-vis the well-known exact algorithm MTU2.

A hybrid algorithm for the unbounded knapsack problem

This paper presents a new approach for exactly solving the Unbounded Knapsack Problem (UKP) and proposes a new bound that was proved to dominate the previous bounds on a special class of UKP instances. Integrating bounds within the framework of sparse dynamic programming led to the creation of an efficient and robust hybrid algorithm, called EDUK2. This algorithm takes advantage of the majority of the known properties of UKP, particularly the diverse dominance relations and the important periodicity property. Extensive computational results show that, in all but a very few cases, EDUK2 significantly outperforms both MTU2 and EDUK, the currently available UKP solvers, as well the well-known general purpose mathematical programming optimizer CPLEX of ILOG. These experimental results demonstrate that the class of hard UKP instances needs to be redefined, and the authors offer their insights into the creation of such instances.

Duration calculus: a real-time semantic for B

Among the possible approaches for expressing real-time problems with the B method, two are dominant : the use of the usual B mechanisms to define real-time constraints on the one hand, and extending B through another formalism more adapted to the real-time context on the other hand. We define here a possible real-time semantic for B, by using a real-time logic (the duration calculus), and we illustrate how this extension affects the proof mechanism used to show the soundness of abstract machines.

Optimal protein threading by cost-splitting

In this paper, we use integer programming approach for solving a hard combinatorial optimization problem, namely protein threading. For this sequence-to-structure alignment problem we apply cost-splitting technique to derive a new Lagrangian dual formulation. The optimal solution of the dual is sought by an algorithm of polynomial complexity. For most of the instances the dual solution provides an optimal or near-optimal (with negligible duality gap) alignment. The speed-up with respect to the widely promoted approach for solving the same problem in [17] is from 100 to 250 on computationally interesting instances. Such a performance turns computing score distributions, the heaviest task when solving PTP, into a routine operation.

BRILLANT: an open source and XML-based platform for rigourous software development

The need for the B method first appeared in industry, and several commercial tools have been developed to support this formalism. However, few of these tools allow reasoning on the formalism itself or on its possible extensions. This article presents an open-source platform, with a focus on the platforms core component, the BCaml project. The tools presented are used to show how very different approaches can be brought together around a central design to form a consistent toolbox, and can be used to develop safe systems, from their specifications to their validation and the generation of safe code.

Recent Advances in Solving the Protein Threading Problem

The fold recognition methods are promissing tools for capturing the structure of a protein by its amino acid residues sequence but their use is still restricted by the needs of huge computational resources and suitable efficient algorithms as well. In the recent version of FROST (Fold Recognition Oriented Search Tool) package the most efficient algorithm for solving the Protein Threading Problem (PTP) is implemented due to the strong collaboration between the SYMBIOSE group in IRISA and MIG in Jouy-en-Josas. In this paper, we present the diverse components of FROST, emphasizing on the recent advances in formulating and solving new versions of the PTP and on the way of solving on a computer cluster a million of instances in a easonable time.

On the parallel prediction of the RNA secondary structure

Publisher Summary This chapter discusses the parallelization of the Vienna package algorithm that predicts the secondary structure of the RNA. Before the tool can be effectively used, it must be tuned on the target architecture. This tune consists of finding the tile sizes for optimal executions. The analytical model is developed to find these optimal tile sizes. The validity of the analytical model developed for the parallel algorithms presented is studied through an extensive set of experiments performed on a Origin 3000. A statistical model is presented, to deal with the cases where the hypothesis of the analytical model is not satisfied. The algorithms are satisfactorily applied to real sequences. The algorithm is applied to real sequences. The speedups, although satisfactory, do not scale for some of those instances— that is, p 3 8. This is probably due to the use of a common static tile size. A dynamic variable tile size on every macro-rectangle is introduced in the chapter.