![]() So this graph is built from a synthetic data set that contains the reads that we made by taking all the 6-mers of the genome. Here's our overlap graph from the previous lecture. It would be a reconstruction of the original genome sequence. So if we took our sequencing reads and we gave them to this algorithm, and asked the algorithm to find their shortest common superstring, then the solution to the problem, the shortest common superstring problem, would also be an assembly of the genome. So let's say for a moment that we have an algorithm for finding the shortest common superstring of a set of strings, and we'll discuss such an algorithm soon. So, it turns out this is the shortest common superstring, so this is a string that contains all the input strings as substrings and there is no shorter string that does this, that contains all the input strings. So this is a string that contains all the input strings as substrings but it's not the shortest. Well, if we didn't have the requirement that the superstring be the shortest superstring, then this problem would be easy, we could simply concatenate all the strings in the set S. So for example, here I have some strings and I'd like to know their shortest common superstring, the shortest string that contains each of these strings as a substring. Given a collection of input strings, a set of input strings, we'd like to find the shortest string that contains all of our input strings, as substrings. So the shortest common superstring problem is this. So, the computational problem is called the shortest common superstring problem, which will sometimes abbreviate as SCS. Kind of in the same way that the naive exact matching problem wasn't perfect, but it was good starting point for our discussion of read alignment. ![]() This first formulation won't be perfect, but it'll be a good starting point for our discussion of the assembly problem. We're now at the point where we can formulate a computational problem that when we solve it, will in turn solve the genome assembly problem. ![]()
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