Computing polygonal path simplification under area measures

In this paper, we consider the restricted version of the well-known 2D line simplification problem under area measures and for restricted version. We first propose a unified definition for both of sum-area and difference-area measures that can be used on a general path of n vertices. The optimal simplification runs in O(n) under both of these measures. Under sum-area measure and for a realistic input path, we propose an approximation algorithm of O n 2 time complexity to find a simplification of the input path, where is the absolute error of this algorithm compared to the optimal solution. Furthermore, for difference-area measure, we present an algorithm that finds the optimal simplification in O(n) time. The best previous results work only on x-monotone paths while both of our algorithms work on general paths. To the best of our knowledge, the results presented here are the first subcubic simplification algorithms on these measures for general paths. 2012 Elsevier Inc. All rights reserved.