Path Simplification Under Difference Area Measure

In this paper, we consider path simplification problem under difference area (diff-area) measure. Dill-area measure is defined as vertical bar A(A) (Q) - A(B)(Q)vertical bar, where A(A)(Q) is the area under Q and above P and A(B)(Q) is the area above Q and under P (see Figure 1). Bose et al. [1] presented an approximation algorithm for finding a simplified path with at most k vertices that minimizes the dill-area measure which only works on x-monotone paths. The constraint of being x-monotone is restrictive in some applications like tracking bird migration paths or map boundary simplification. Here, we extend the method of Bose et al. [1] and present algorithms with the same time complexities as theirs for general paths.