Systèmes interactifs pour la résolution de problèmes complexes.

Abstract : This thesis focuses on algorithm-expert interaction for solving hard problems. Several definitions of an "expert" are possible. Our work concerns interactions with an oracle (rather than human) expert, as we are looking for theoretical performance guarantee. Thus, we are interested in tradeoffs between performance, cost (typically running time), and length of information provided by the oracle. The first objective of this thesis is to understand what is the related work and the common oracle techniques in different domains (distributed and online computing, complexity, combinatorial optimization). The second objective is centered on combinatorial optimization, and more precisely on scheduling and packing problems. We aim at showing how this interactive setting is helpful for the design of approximation algorithms, and of course to provide new results on scheduling and packing problems using these techniques. We mainly focused on two problems: the discrete Resource Sharing Scheduling Problem ($dRSSP$) and the Multiple Strip Packing ($MSP$). The $dRSSP$ comes from the community of hybridation of algorithms. Given a set of algorithms (often called a portfolio), a fixed amount of resources (processors for example), and a (finite) benchmark of instances to solve, the goal is to distribute the resources among the processors to minimize the cost for solving the whole benchmark, using a "space sharing" model for running the algorithms in parallel. We studied the impact of different questions to ask to the oracle, and how to communicate "efficiently" (meaning that the oracle answer is short) with the oracle, leading to several approximation schemes. $MSP$, which is an extension of the well known strip packing problem, consists in packing rectangles into a fixed number of strips, minimizing the height of the packing. We provided approximation schemes/algorithms for different variants of $MSP$ where strips have equal/different widths, and where rectangles must be packed continuously or not (corresponding then to scheduling parallel jobs). It turns out that interactive techniques point out the difficulty of the problems, and are helpful to study problems in a different ways.
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https://tel.archives-ouvertes.fr/tel-00543195
Contributor : Marin Bougeret <>
Submitted on : Monday, December 6, 2010 - 10:06:11 AM
Last modification on : Friday, May 3, 2019 - 12:08:01 PM
Long-term archiving on : Monday, November 5, 2012 - 11:26:19 AM

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Marin Bougeret. Systèmes interactifs pour la résolution de problèmes complexes.. Autre [cs.OH]. Institut National Polytechnique de Grenoble - INPG, 2010. Français. ⟨tel-00543195⟩

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