Using oracles for the design of efficient approximation algorithms

Abstract : We are interested here in oracle techniques for the design of approximation algo- rithms. Following the classical definition, an oracle is a black box capable of answering correctly and instantaneously any question. Several classical approximation scheme de- sign techniques (typically PTAS) can be revisited using oracle. Our objective in this work is to show that, conversely, oracle techniques are not limited to the design of PTAS. In particular, interactivity (using queries to oracle) may also lead to parameterized algorithm (whose complexity is exponential in a parameter, supposed to be "small"), that can be more practical than classical P T AS. Moreover, we aim at showing how it is possible to "degenerate" questions asked to the oracle to derive fast implementations of these interactive algorithms. These ideas will be illustrated on the classical makespan minimization on uniform machines problem (QCmax ).
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Marin Bougeret, Pierre-Francois Dutot, Denis Trystram. Using oracles for the design of efficient approximation algorithms. MAPSP: Models and Algorithms for Planning and Scheduling Problems, Jun 2011, Nymburk, Czech Republic. ⟨hal-00738513⟩

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