In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

Calculating distance pairs is O(n2) in memory and time and finding the nearest neighbor is O(n) in time. Tree indexing techniques like kd-tree [2] were developed to cope with large n, however their performance quickly breaks down for p > 3 [3]. Locality sensitive hashing (LSH) [3] is a technique for generating hash numbers from high dimensional data, such that nearby points have identical hashe...