Maximum weight independent set in trees
Computing a maximum independent set, weighted or unweighted, is NP-hard for general as well as planar graphs. However, polynomial time algorithms do exist for solving this problem on special classes of graphs. In this paper we present an efficient algorithm for computing a maximum wehe extent to which, given two categories A and B and a functor K from A to B, the functor K can be used to gain information on the objects of B via approximations by K-images of objects in A. In the shape geometric theory of Borsuk the category A is the homotopy category of polyhedra, B the homotopy category of compact metric spaces and K is the inclusion. In this note the authors set out to interpret the simpler parts of categorical shape theory in terms of the basic theoretical problems of pattern recognition, namely the classification and recognition problems. In this interpretation A is a category of archetypes or models whilst B is a category of objects of interest, K being a ``comparison functor''. The consequences of such a basic recognition system are explored and certain problems that naturally occur in this theory are discussed with reference to pattern recognition. The authors intend to write further notes of this form in the expectation that the ideas, suitably modified, may prove to be of use within the theory of pattern recognition. The authors would like to point out that reference 2 is to be published under the title ``Shape theory: Categorical approximation methods'' by Ellis Horwood Ltd. (expected publication date Spring 1989).
maximum wehe extent to which, given two categories A and B and a functor K from A to B, the functor K can be used to gain information on the objects of B via approximations by K-images of objects in A. In the shape geometric theory
scientific article; zbMATH DE number 4047156
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