Abstract — Placement of Numbers on a Grid

With increasing dependency on technology and data storage, efficient and searchable storage methods grow in importance. My project involves sorting data placement on a grid model. My project uses a 5 by 5 grid, whose 25 points are labeled 1 through 25. The goal is to return scattered numbers to their original positions in the fewest number of moves.  I will also try situations in which each number is within a bounded distance from its original position. I will begin with a 2 by 2 grid and progress to grids with more points, looking for helpful patterns to efficiently return all numbers to their original positions. The ultimate goal is to find an optimal sorting method for grids of any size.