Hybrid tractability of soft constraint problems

The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint problems are a generalisation of the CSP which allow the user to model optimisation problems. Considerable effort has been made in identifying properties which ensure tractability in such problems. In this work, we initiate the study of hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but which do not depend only on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity). We present several novel hybrid classes of soft constraint problems, which include a machine scheduling problem, constraint problems of arbitrary arities with no overlapping nogoods, and the SoftAllDiff constraint with arbitrary unary soft constraints. An important tool in our investigation will be the notion of forbidden substructures.Comment: A full version of a CP'10 paper, 26 page

Temperature-based metallicity measurements at z=0.8: direct calibration of strong-line diagnostics at intermediate redshift

We present the first direct calibration of strong-line metallicity diagnostics at significant cosmological distances using a sample at z=0.8 drawn from the DEEP2 Galaxy Redshift Survey. Oxygen and neon abundances are derived from measurements of electron temperature and density. We directly compare various commonly used relations between gas-phase metallicity and strong line ratios of O, Ne, and H at z=0.8 and z=0. There is no evolution with redshift at high precision ($\Delta \log{\mathrm{O/H}} = -0.01\pm0.03$, $\Delta \log{\mathrm{Ne/O}} = 0.01 \pm 0.01$). O, Ne, and H line ratios follow the same locus at z=0.8 as at z=0 with $\lesssim$0.02 dex evolution and low scatter ($\lesssim$0.04 dex). This suggests little or no evolution in physical conditions of HII regions at fixed oxygen abundance, in contrast to models which invoke more extreme properties at high redshifts. We speculate that offsets observed in the [N II]/H$\alpha$ versus [O III]/H$\beta$ diagram at high redshift are therefore due to [NII] emission, likely as a result of relatively high N/O abundance. If this is indeed the case, then nitrogen-based metallicity diagnostics suffer from systematic errors at high redshift. Our findings indicate that locally calibrated abundance diagnostics based on alpha-capture elements can be reliably applied at z$\simeq$1 and possibly at much higher redshifts. This constitutes the first firm basis for the widespread use of empirical calibrations in high redshift metallicity studies.Comment: 14 pages, 10 figures, accepted to Ap

Fundamental properties of neighbourhood substitution in constraint satisfaction problems

AbstractIn combinatorial problems it is often worthwhile simplifying the problem, using operations such as consistency, before embarking on an exhaustive search for solutions. Neighbourhood substitution is such a simplification operation. Whenever a value x for a variable is such that it can be replaced in all constraints by another value y, then x is eliminated.This paper shows that neighbourhood substitutions are important whether the aim is to find one or all solutions. It is proved that the result of a convergent sequence of neighbourhood substitutions is invariant modulo isomorphism. An efficient algorithm is given to find such a sequence. It is also shown that to combine consistency (of any order) and neighbourhood substitution, we only need to establish consistency once

Tractable constraints on ordered domains

AbstractFinding solutions to a constraint satisfaction problem is known to be an NP-complete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. In this paper we identify a restricted set of contraints which gives rise to a class of tractable problems. This class generalizes the notion of a Horn formula in propositional logic to larger domain sizes. We give a polynomial time algorithm for solving such problems, and prove that the class of problems generated by any larger set of constraints is NP-complete

Kaon Electromagnetic Production on Nuclei

The formation and excitation of hypernuclei through kaon photoproduction is reviewed. Basic features of the production process are emphasized. The possibility of extracting new information on hypernuclear structure and on the wave function of the bound $\Lambda$ is discussed. New results are presented for the quasifree production process $A(\gamma, K \Lambda)B$. Observables of this reaction are shown to be sensitive to the $\Lambda$-nucleus final state interaction.Comment: 10 pages, 4 figures. Invited talk given at the International Conference on Hypernuclear and Strange Particle Physics (HYP97), Brookhaven National Laboratory, USA, October 13-18, 1997. To be published in Nucl. Phys.

The interpretations of line drawings with contrast failure and shadows

Abstract. In line drawings derived from real images, lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources. This paper shows that it is the presence of shadows, rather than contrast failure, that renders the line drawing labelling problem NP-complete. However, shadows are a valuable visual cue, since their presence is formally shown to reduce the average ambiguity of drawings. This is especially true when constraints concerning shadow formation are employed to differentiate shadow and non-shadow lines. The extended junction constraint, concerning straight lines colinear with junctions, compensates the loss of information caused by contrast failure. In fact, we observe the contrast failure paradox: a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure. It is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing. This paper shows that these coplanarity constraints are robust to the presence of contrast failure

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