Solving Temporal Puzzles

Abstract

Many physical phenomena, within short time windows, can be explained by low order differential relations. In a discrete world, these relations can be described using low order difference equations or equivalently low order auto regressive (AR) models. In this paper, based on this intuition, we propose an algorithm for solving time-sort temporal puzzles, defined as scrambled time series that need to be sorted out. We frame this highly combinatorial problem using a mixed-integer semi definite programming formulation and show how to turn it into a mixed-integer linear programming problem by using the recently introduced atomic norm framework. Our experiments show the effectiveness and generality of our approach in different scenarios.