Let P be a set of n points, where each point is colored with one the k possible colors. We present efficient algorithms to preprocess such that for given query q, we can quickly identify smallest color spanning object desired type containing q. In this paper, focus on (i) intervals, (ii) axis-parallel square, (iii) rectangle, (iv) equilateral triangle fixed orientation and (v) circle, as our ob...

Abstract Ensemble Kalman inversion (EKI) is an adaption of the ensemble filter (EnKF) for numerical solution inverse problems. Both EKI and EnKF suffer from ‘subspace property’, i.e. solutions are linear combinations initial ensembles. The subspace property implies that size should be larger than problem dimension to ensure EKI’s convergence correct solution. This scaling impractical prevents u...