Some complexity and approximation results for coupled-tasks scheduling problem according to topology

We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,. . .). In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters

Scheduling stretched coupled-tasks with compatibilities constraints : model, complexity and approximation results for some class of graphs

We tackle the makespan minimization coupled-tasks problem in presence of compatibility constraints. In particular, we focus on stretched coupled-tasks, {\it i.e.}coupled-tasks having the same sub-tasks execution time and idle time duration. We study severals problems in frame works of classic complexity and approximation for which the compatibility graph $G_c$ is bipartite (star, chain, $\ldots$) In such context, we design some efficient polynomial-time approximation algorithms according to difference parameters of the scheduling problem. When $G_c$ is a $k$-stage bipartite graph, we propose, among other, a $\frac{7}{6}$-approximation algorithm when $k=1$, and a $\frac{13}{9}$-approximation algorithm when $k=2$.\

On the complexity of Wafer-to-Wafer Integration

In this paper we consider the Wafer-to-Wafer Integration problem. A wafer can be seen as a pp-dimensional binary vector. The input of this problem is described by mm multisets (called “lots”), where each multiset contains nn wafers. The output of the problem is a set of nn disjoint stacks, where a stack is a set of mm wafers (one wafer from each lot). To each stack we associate a pp-dimensional binary vector corresponding to the bit-wise AND operation of the wafers of the stack. The objective is to maximize the total number of “1” in the nn stacks. We provide m1−ϵm1−ϵ and p1−ϵp1−ϵ non-approximability results even for n=2n=2, f(n)f(n) non-approximability for any polynomial-time computable function ff, as well as a View the MathML sourcepr-approximation algorithm for any constant rr. Finally, we show that the problem is View the MathML sourceFPT when parameterized by pp, and we use this View the MathML sourceFPT algorithm to improve the running time of the View the MathML sourcepr-approximation algorithm

Software (re)modularization: Fight against the structure erosion and migration preparation

Software systems, and in particular, Object-Oriented sys- tems are models of the real world that manipulate representa- tions of its entities through models of its processes. The real world is not static: new laws are created, concurrents offer new functionalities, users have renewed expectation toward what a computer should offer them, memory constraints are added, etc. As a result, software systems must be continuously updated or face the risk of becoming gradually out-dated and irrelevant [34]. In the meantime, details and multiple abstraction levels result in a high level of com- plexity, and completely analyzing real software systems is impractical. For example, the Windows operating system consists of more than 60 millions lines of code (500,000 pages printed double-face, about 16 times the Encyclopedia Universalis). Maintaining such large applications is a trade- off between having to change a model that nobody can understand in details and limiting the impact of possible changes. Beyond maintenance, a good structure gives to the software systems good qualities for migration towards modern paradigms as web services or components, and the problem of architecture extraction is very close to the classical remodularization problem

ordonnancement et communications

Cette HDR concerne l'ordonnancement en présence de divers communication

General Scheduling Non-Approximability Results in Presence of Hierarchical Communications

International audienc

On the Linearization of Scaffolds Sharing Repeated Contigs

International audienceScaffolding is the final step in assembling Next Generation Sequencing data, in which pre-assembled contiguous regions (“contigs”) are oriented and ordered using information that links them (for example, mapping of paired-end reads). As the genome of some species is highly repetitive, we allow placing some contigs multiple times, thereby generalizing established computational models for this problem. We study the subsequent problems induced by the translation of solutions of the model back to actual sequences, proposing models and analyzing the complexity of the resulting computational problems. We find both polynomial-time and $NP$ -hard special cases like planarity or bounded degree

An Approximate Algorithm for the Precedence Constrained Scheduling Problem with Hierarchical Communications

International audienceWe study the problem of minimizing the makespan for the precedence multiprocessor constrained scheduling problem with hierarchical communications (Parallel Process. Lett. 10(1) (2000) 133). We propose an approximation algorithm for the Unit Communication Time hierarchical problem with arbitrary but integer processing times and an unbounded number of biprocessor machines. We extend this result in the case where each cluster has m processors (where m is a fixed constant) by presenting a (2−2/(2m+1))-approximation algorithm

The Workforce Routing and Scheduling Problem: solving real-world Instances

International audienceWe propose an efficient method to solve a workforce routing and scheduling problem with working constraints, and a bounded execution time limit. This problem combines two fundamental problems in operations research: routing and scheduling. In such a context, we develop a column generation algorithm, as a set partitioning problem with side constraints, within a branch-and-price framework. The pricing sub-problem is an elementary shortest path with resource constraints modeled with constraint programming. In our branch-and-price framework, we first solve our problem using branch-and-price and a branch-and-bound strategy is proposed on the last restricted master problem, in order to obtain a feasible solution when the time limit is almost reached. However, we show that the developed method leads to better solutions than using constraint programming or large neighborhood search methods. We show the relevance of our method with various-size real instances