Networks of constraints: Fundamental properties and applications to picture processing

Abstract

The problem of representation and handling of constraints is here considered, mainly for picture processing purposes. A systematic specification and utilization of the available constraints could significantly reduce the amount of search in picture recognition. On the other hand, formally stated constraints can be embedded in the syntactic productions of picture languages.Only binary constraints are treated here, but they are represented in full generality as binary relations. Constraints among more than two variables are then represented as networks of simultaneous binary relations. In general, more than one equivalent (i.e., representing the same constraint) network can be found: a minimal equivalent network is shown to exist, and its computation is shown to solve most practical problems about constraint handling.No exact solution for this central problem was found. Anyway, constraints are treated algebtaically, and the solution of a system of linear equations in this algebra provides an approximation of the minimal network. This solution is then proved exact in special cases, e.g., for tree-like and series parallel networks and for classes of relations for which a distributive property holds. This latter condition is satisfied in cases of practical interest.

Information Support of FMS Configuration Design

“…A DCN ~ is a sequence of static CNs l(O)""'(a).l(a).l(a+l)"'" each resulting from a change in the preceding one imposed by "the outside world". The task of finding a solution in a DCN is NP-complete, so a number oflocal consistency algorithms are proposed (Mackworth, 1977;Montanari, 1974). The most widely used are those achieving arc-consistency, which check the consistency of values for each pair of variables linked by a constraint.…”

“…The most widely used are those achieving arc-consistency, which check the consistency of values for each pair of variables linked by a constraint. Arc consistency is very simple to implement and it has good efficiency, described in (Montanari, 1974).…”

Constraint design rewriting

“…In this paper we combine some techniques from ADR and from constraint networks [5,6] in order to accommodate arbitrary notions of constraints, as those used in popular applications such as optimization, knowledge representation, and synchronization, to mention a few [7]. Our proposal can be understood both as (i) an enrichment of ADR with non-spatial constraints, and (ii) an application of the ADR methodology to the design and transformation of structured constraint networks.…”

“…The ability of representing both a graph and its syntax tree is particularly relevant for constraints networks [5,6]. Constraint networks are hyper-graphs whose nodes and hyper-edges are respectively interpreted as variables and relations constraining the assignment of values to the variables of their adjacent nodes.…”

Mass Customization of Services

“…A CSP is a triplet {X, D, C} where X is a set of variables, D is a set of finite domains (one for each variable) and C a set of constraints linking the variables [9]. The variables can be either discrete or continuous.…”