This is actually means that I might be able to put some constraints on the shifts that I need to consider. So commonly used constraints are Sakoe-Chiba band constraint or the Itakura parallelogram constraint. Essentially what the Sakoe-Chiba band constraint is saying that any alignment which basically has a, Limit, in the distance that I'm considering at a given point in time. So basically alignments that are w units in one direction are okay, but any alignment that would require, More than w distance, are not okay. So essentially, what I am saying that when you are aligning the two time streams, you can look w unit before or w unit after for alignment in time. That's okay that my stretching is okay but any stretching that would basically require more than w units is not going to be accepted. That's essentially the idea of the Sakoe-Chiba band and note that basically if you use this constraint. If your w is small essentially it means that you don't necessarily need any to compute very large number of alternatives. So you are only with a good feeling if it is a small band in your time series. Itakura parallelogram is similarly an idea, essentially what it say is, well, you know what? Yes, we wanted window for stretching, but the length of the window should be adaptive. Instead of basically assuming that the length of the window, I need to counter for stretching always w. What we can do is we can assume that, at the beginning, And end of the of the time series, I will basically have very small stretches. So beginning and end, my stretches will be small. But at the center, at the sort of middle of the time series, I might be able to do larger stretches, larger alignment errors. So this essentially means that at the beginning and end of the two time series, the window that I will consider for alignments will be small. However, two of the centers of the both series I will allow large alignment errors, large stretches in one time series or in the other. And in general, Itakura parallelogram essentially works on the general assumption, is that the two time series, essentially the beginning alignment. I mean remember, the extreme in both cases at the very extreme, Essentially I am forced to align the very first strings. So the very first strings the alignment there is 0, right, but as I sort of progress, I might basically do bigger alignment errors. So this assumption is Itakura parallelogram, and both of the are heuristic. So neither one of them basically has very strong theoretical background, but they're essentially both used as heuristic to reduces the order N times M cost of dynamic time warping