Redundancy checking is an important task in the research of knowledge representation and reasoning. In this paper, we consider redundant qualitative constraints. For a set ? of qualitative constraints, we say a constraint ( x R y ) in ? is redundant if it is entailed by the rest of ?. A prime subnetwork of ? is a subset of ? which contains no redundant constraints and has the same solution set as ?. It is natural to ask how to compute such a prime subnetwork, and when it is unique. We show that this problem is in general intractable, but becomes tractable if ? is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of the Region Connection Calculus RCC8 in which weak composition distributes over nonempty intersections, then ? has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from ?. As a by-product, we show that any path-consistent network over such a distributive subalgebra is minimal and globally consistent in a qualitative sense. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms, especially in constraint networks with larger proportions of partial overlap relations.
In research on constraint satisfaction problems (CSPs), there are also many studies of constraint redundancy. While most of this research concerns redundant modelling (e.g., @cite_15 ), @cite_39 studied redundancy modulo a given local consistency. Their paper is close in spirit to ours. Let @math be a CSP and @math a local consistency. call a constraint @math in @math iff @math is @math -inconsistent. Because path-consistency implies consistency for RCC5 8 constraint networks over their maximal tractable subclasses, our notion of redundancy (when restricted to networks over these tractable subclasses) is equivalent to redundancy modulo path-consistency in the sense of @cite_39 .
@cite_15 @cite_39
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A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically implied by others in the problem model. However, some redundant constraints are propagation redundant and hence do not contribute additional propagation information to the constraint solver. Redundant constraints arise naturally in the process of redundant modeling where two models of the same problem are connected and combined through channeling constraints. In this paper, we give general theorems for proving propagation redundancy of one constraint with respect to channeling constraints and constraints in the other model. We illustrate, on problems from CSPlib (http: www.csplib.org), how detecting and removing propagation redundant constraints in redundant modeling can speed up search by several order of magnitudes. In this paper, we propose a new technique to compute irredundant sub-sets of constraint networks. Since, checking redundancy is Co-NP Complete problem, we use different polynomial local consistency entailments for reducing the computational complexity. The obtained constraint network is irredundant modulo a given local consistency. Redundant constraints are eliminated from the original instance producing an equivalent one with respect to satisfiability. Eliminating redundancy might help the CSP solver to direct the search to the most constrained (irredundant) part of the network.