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In this paper we consider a problem of optimal polygonal approximation with a minimum number of the line segments for a given constraint on the total distortion with L2 measure. A fast suboptimal algorithm for the problem is proposed. In order to improve the solution obtained, this algorithm can be used in combination with a Reduced-Search Dynamic Programming algorithm. The experiments with the large size vector data have demonstrated both high efficiency and high time performance of the proposed algorithms for the following practical applications: image vectorization and segmentation, vector maps simplification, vector data compression, digital shapes encoding, etc.