Optimum quantizing of monotonic nondecreasing arrays

Abstract

This paper presents an efficient algorithm for finding the optimal k-cuts of a nondecreasing array of size n that produces the maximum area under the points. The naïve approach uses a dynamic programming algorithm which requires O(kn2) time, where n is the size of the array. This algorithm is time consuming for large n or k and thus inappropriate. We design faster algorithms by discovering and proving some nice properties of the nondecreasing arrays, finding convex hull, and by continuous-to-discrete transformation. We believe that an O(kn) time algorithm exists and show a heuristic algorithm.