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Abstract.This paper deals with the problem of finding a base and strong generating set for the group generated by a given set of permutations. The concepts of base and strong generating set were introduced by Sims [5], [6] and provide the most effective tool for computing with permutation groups of high degree. One algorithm, originally proposed by Sims [7], is described in detail; its behavior on a number of groups is studied, and the influence of certain parameters on its performance is investigated. Another algorithm, developed by the author, is given, and it is shown how the two algorithms may be combined to yield an exceptionally fast and effective method.

Abstract. This paper presents a novel algorithm intended to generate kconnected skeletons of a digital binary image using a new mask set. These skeletons may be 4 or 8 connected. The new algorithm performs a thinning process that finish when it is not possible to eliminate additional pixels without breaking the connectivity. The end-point criterion and a 3x3 masks set are used to decide if a pixel is eliminated. The proposed masks set for each kind of connectivity covers all the necessary cases, and guarantee to obtain a one pixel wide and k-connected skeleton without parasitic branches. The new algorithm yields some advantages to developers. It is not just oriented to written characters or some kind of object in particular; this means that the algorithm can be adapted easily to any application generating good results. Besides, the user can work with different classes of connectivity; note that several recent algorithms use 4-connectivity while 8-connectivity is used for others. Additionally, the skeletons produced by the new algorithm are immune to structured noise around the processed objects.