Retour sur trace

Résumé

En informatique, plus précisément en algorithmique, le retour sur trace ou retour arrière (appelé aussi backtracking en anglais) est une famille d'algorithmes pour trouver des solutions à des problèmes algorithmiques, notamment de satisfaction de contraintes. Contrairement à une recherche exhaustive, un algorithme de retour sur trace construit incrémentalement des solutions candidates. Il abandonne la construction lorsqu'il ne peut compléter le candidat courant en solution valide. Il revient alors sur ses choix (d'où le nom de retour sur trace) et en prend d'autres pour construire d'autres solutions candidates. Le retour sur trace est utilisé pour résoudre des problèmes algorithmiques difficile à résoudre, typiquement NP-complets. Principe Ces algorithmes permettent de tester systématiquement l'ensemble des affectations potentielles du problème. Ils consistent à sélectionner une variable du problème, et pour chaque affectation possible de cette variable,

Source officielle

https://fr.wikipedia.org/wiki/Retour_sur_trace

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Séances de cours associées (9)

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A catalog of minimally nonideal matrices

François Margot

This paper describes a backtracking algorithm for the enumeration of nonisomorphic minimally nonideal (n2n) matrices that are not degenerate projective planes. The application of this algorithm for nh12 yielded 20 such matrices, adding 5 matrices to the 15 previously known. For greater dimensions, n=14 and n=17, 13 new matrices are given. For nonsquare matrices, 38 new minimally nonideal matrices are described.

1998

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Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron

Thomas Liebling, François Margot

In this paper, we investigate the applicability of backtrack technique for solving the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is apolynomial in the input size, but the vertex enumeration problem requires a backtrack algorithm to solve a decision problem, called the restricted vertex problem, for each output, which is shown to be NP-complete. Some related NP-complete problems associated with a system of linear inequalities are also discussed, including the optimal vertex problems for polyhedra and arrangements of hyperplanes.

1994

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Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron

Thomas Liebling, François Margot

In this paper, we investigate the applicability of backtrack technique to solve the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is polynomial in the input size, but the vertex enumeration problem requires a backtrack algorithm to solve a decision problem, called the restricted vertex problem, for each output, which is shown to be NP-complete. Some related NP-complete problems associated with a system of linear inequalities are also discussed, including the optimal vertex problems for polyhedra and arrangements of hyperplanes.

1997

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