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Notes:


So what we are going to do is to construct a graph with only clockwise cycles, such a graph will contain only cycles with sum of edge weights t > 0. Here is the graph that we construct. It’s easier to see the structure of this graph in the right picture. We divide the graph into 4 quadrants, and in each quadrant we include all possible edges but only in the shown direction. Here is an example of a cycle in this graph. So our windows that we will optimize over are defined through the cycles in this graph, these are all the windows given by the inside area of some cycle in this graph. We call our windows compact. Since there is 1-to-1 correspondence between cycles and windows, we can find the optimal one by running MCR algorithm. Note that the size of the graph gives us the largest allowed window shape.