title: an algorithm for fitting a rectangle inside a polygon
body: <p>I have a kind of cutting problem. There is an irregular polygon that doesn't have any holes and a list of standard sized of rectangular tiles and their values.</p>
  
  <p>I want an efficient algorithm to find the single best valued tile that fit in this polygon; or an algorithm that just says if a single tile can fit inside the polygon. And it should run in deterministic time for irregular polygons with less than 100 vertices. </p>
  
  <p>Please consider that you can rotate the polygon and tiles.
  Answers/hints for both convex and non-convex polygons are appreciated.</p>