On Broken Triangles (IJCAI 2016)

International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP

Sur la complexité des algorithmes de backtracking et quelques nouvelles classes polynomiales pour CSP

National audienceThe question of tractable classes of constraint satisfaction problems (CSPs) has been studied for a long time, and is now a very active research domain. However, studies of tractable classes are typically very theoretical. They usually introduce classes of instances together with polynomial time algorithms for recognizing and solving them, and the algorithms can be used only for the new class. In this paper, we address the issue of tractable classes of CSPs from a di erent perspective. We investigate the complexity of classical, generic algorithms for solving CSPs (such as Forward Checking). We introduce a new parameter for measuring their complexity and derive new complexity bounds. By relating the com- plexity of CSP algorithms to graph-theoretic parameters, our analysis allows us to point at new tractable classes, which can be solved directly by the usual CSP algorithms in polynomial time, and without the need to recognize the classes in advance.L'étude des classes polynomiales, pour les problèmes de satisfaction de contraintes (CSP), constitue depuis longtemps un domaine de recherche important qui s'avère aujourd'hui très actif. Cependant, les travaux réalisés jusqu'à présent se sont révélés pour l'essentiel théoriques. En effet, ils se cantonnent en général à la définition de classes d'instances pour lesquelles des algorithmes polynomiaux ad hoc, à la fois pour la reconnaissance et pour la résolution, sont proposes. Ces algorithmes ne peuvent être, en fait, utilisés que pour le traitement d'une classe d'instances donnée. Ils s'avèrent ainsi difficilement exploitables en pratique, et ne sont donc pas exploités au sein de solveurs généraux. L'intérêt pratique des classes polynomiales est ainsi très limitée. Dans cet article, nous abordons la question des classes polynomiales CSP d'un point de vue différent de l'approche classique, en nous intéressant aux algorithmes que l'on peut retrouver dans les systèmes de résolution opérationnels. Pour cela, nous _étudions d'abord la complexité d'algorithmes génériques de résolution de CSP tels que le Forward-Checking par exemple. Cette étude s'appuie sur l'exploitation d'un paramètre issu de la théorie des graphes, et qui permet de proposer de nouvelles bornes de complexité. La mise en relation de ces nouvelles bornes avec certains résultats issus de la théorie des graphes nous permet d'exhiber de nouvelles classes polynomiales. De cette façon, nous montrons comment des algorithmes classiques de résolution de CSP peuvent traiter efficacement en pratique ainsi qu'en théorie, des instances de CSP, sans devoir reconnaître au préalable leur appartenance à d'éventuelles classes polynomiales

Autour des Triangles Cassés

National audienceUne instance CSP binaire qui satisfait la propriété des triangles cassés (BTP) peut etre résolue en temps polynomial. Malheureusement, en pratique, peu d'ins-tances satisfont cette propriété. Nous montrons qu'une version locale de BTP permet de fusionner des valeurs dans les domaines d'instances binaires quelconques. Des expérimentations démontrent la diminution significative de la taille de l'instance pour certaines classes de pro-bì emes. Ensuite, nous proposons une généralisation de cette fusion a des contraintes d'arité quelconque. En-fin, une version orientée nous permet d'´ etendre la classe polynomiale BTP. Ce papier est un résumé de l'article M. C. Cooper, A. El Mouelhi, C. Terrioux et B. Zanuttini. On Broken Triangles In Proceedings of CP,LNCS 8656, 9–24, 2014

On the Efficiency of Backtracking Algorithms for Binary Constraint Satisfaction Problems

International audienceThe question of tractable classes of constraint satisfaction problems (CSPs) has been studied for a long time, and is now a very active research domain. However, studies of tractable classes are typically very theoretical. They usually introduce classes of instances together with polynomial time algorithms for recognizing and solving them, and the algorithms can be used only for the new class. In this paper, we address the issue of tractable classes of CSPs from a different perspective. We investigate the complexity of classical, generic algorithms for solving CSPs (such as Forward Checking). We introduce a new parameter for measuring their complexity and derive new complexity bounds. By relating the complexity of CSP algorithms to graph-theoretic parameters, our analysis allows us to point at new tractable classes, which can be solved directly by the usual CSP algorithms in polynomial time, and without the need to recognize the classes in advance

On Broken Triangles

A binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP

EFFECT OF SALINITY STRESS ON GERMINATION OF FIVE TUNISIAN LENTIL (LENS CULINARIS L.) GENOTYPES

Salinity is one of the major stresses especially in arid and semi-arid regions, which severely limites crop production. It is a significant problem affecting agriculture worldwide and is predicted to become a larger problem in the coming decades. This study was conducted to assess the effect of different salinity level (0, 50, 150, 250 mMol of NaCl) on lentil seed germination efficiency (germination, seedling shoot length, seedling root length, seedling fresh shoot weight and seedling fresh root weight). Five Tunisian genotypes of lentil (Lens culinaris M) namely: Kef, Siliana, Nefza, Ncir, and Local oueslatia were investigated. Results showed that there were significant differences among the different NaCl solution for all evaluated traits. Indeed, the experiment showed that the concentrations of salt have a negative impact on the germination and growth of lentil. As a result when the concentration of salt increases, the germination, length of root and shoot and fresh weight of root and shoot decreases. At 250 mM salt stress level, seed germination percentage of all genotypes was notably reduced compared with non-stress condition (0.0 mMol). Moreover, the seeds were not germinated by the 250 mM salinity level for kef genotype. From the results of this present investigation, it can be concluded that seeds of Kef and Ncir genotypes were susceptible to higher concentrations of salt solutions in germination stage. However, Siliana, Local oueslatia and Nefza genotypes can be considered as tolerant to salt stress compared to the other ones. These genotypes could be used for further analysis and for hybridization in the breeding program for enhancing lentil cultivation in newly reclaimed soils

Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems

International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in arbitrary instances of binary CSP, thus providing a novel polynomial-time reduction operation. Extensive experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity and we investigate the theoretical relationship with resolution in SAT. A directional version of general-arity BTP-merging then allows us to extend the BTP tractable class previously defined only for binary CSP. We investigate the complexity of several related problems including the recognition problem for the general-arity BTP class when the variable order is unknown, finding an optimal order in which to apply BTP merges and detecting BTP-merges in the presence of global constraints such as AllDifferent

EFFECT OF SALINITY STRESS ON GERMINATION OF FIVE TUNISIAN LENTIL (LENS CULINARIS L.) GENOTYPES

Salinity is one of the major stresses especially in arid and semi-arid regions, which severely limites crop production. It is a significant problem affecting agriculture worldwide and is predicted to become a larger problem in the coming decades. This study was conducted to assess the effect of different salinity level (0, 50, 150, 250 mMol of NaCl) on lentil seed germination efficiency (germination, seedling shoot length, seedling root length, seedling fresh shoot weight and seedling fresh root weight). Five Tunisian genotypes of lentil (Lens culinaris M) namely: Kef, Siliana, Nefza, Ncir, and Local oueslatia were investigated. Results showed that there were significant differences among the different NaCl solution for all evaluated traits. Indeed, the experiment showed that the concentrations of salt have a negative impact on the germination and growth of lentil. As a result when the concentration of salt increases, the germination, length of root and shoot and fresh weight of root and shoot decreases. At 250 mM salt stress level, seed germination percentage of all genotypes was notably reduced compared with non-stress condition (0.0 mMol). Moreover, the seeds were not germinated by the 250 mM salinity level for kef genotype. From the results of this present investigation, it can be concluded that seeds of Kef and Ncir genotypes were susceptible to higher concentrations of salt solutions in germination stage. However, Siliana, Local oueslatia and Nefza genotypes can be considered as tolerant to salt stress compared to the other ones. These genotypes could be used for further analysis and for hybridization in the breeding program for enhancing lentil cultivation in newly reclaimed soils

Variable and value elimination in binary constraint satisfaction via forbidden patterns

Variable or value elimination in a constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. A variable elimination rule (value elimination rule) allows the polynomial-time identification of certain variables (domain elements) whose elimination, without the introduction of extra compensatory constraints, does not affect the satisfiability of an instance. We show that there are essentially just four variable elimination rules and three value elimination rules defined by forbidding generic sub-instances, known as irreducible existential patterns, in arc-consistent CSP instances. One of the variable elimination rules is the already-known Broken Triangle Property, whereas the other three are novel. The three value elimination rules can all be seen as strict generalisations of neighbourhood substitution.Comment: A full version of an IJCAI'13 paper to appear in Journal of Computer and System Sciences (JCSS