Finding Maximum and Minimum Size Matrices: The Algorithmic Complexity of Coding Challenges

We investigate coding challenge problems related to finding a maximum (or minimum) size match for a predetermined two-dimensional pattern. We improve upon known runtime results by introducing new algorithms and refining existing algorithmic techniques. First, we present our main result which introduces a nearly quadratic time algorithm for the problem of finding a rectangular block within a matrix of maximum (or minimum) size containing only positive border entries which improves the prior cubic time solution. Then, we introduce a quadratic time and linear space algorithm for the problem of finding all rectangular blocks containing only positive border and empty interior entries. Finally, we present a log(n) factor improvement for detecting the largest length such that all square blocks in a matrix have their sums bounded by a given number.