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<blockquote data-quote="Pickaxe" data-source="post: 2174262" data-attributes="member: 10812">I have no background in this whatsoever, so forgive me if this is of absolutely no help.If you think of the set of all possible 4d6 drop the lowest characters as defining a multivariate &quot;character space&quot;, can you create an algorithm that can eliminate parts of that space (worthless characters) from consideration for subsequent calculations? For instance, any character with three scores of 3 is &quot;worthless,&quot; regardless of the other scores, so, you could just ignore all characters with three 3s and have that many fewer calculations to make.The only reason I'm suggesting this is that it sounds like a problem that biologists run into when trying to analyze evolutionary relationships. You have a matrix of organisms and scores for various traits, and you can create &quot;trees&quot; that are networks implying certain changes in traits, or steps. The tree with the fewest steps is considered to be best, so you can use a computer to find the tree with the fewest steps. That's easy for three organisms, for which there are only three possible combinations, but, as you increase the number of organisms in the analysis, the number of possible trees increases by a sort of factorial progression. Thus, looking at every possible tree becomes impractical in terms of time. One solution is an algorithm called &quot;branch-and-bound&quot;, which basically finds the shortest tree by a process analogous to what I described above. I forget the details of how it works at the moment, but someone familiar with graph theory may know these things; apparently similar algorithms are used for telecommunications networks.--Axe</blockquote>

[QUOTE="Pickaxe, post: 2174262, member: 10812"] I have no background in this whatsoever, so forgive me if this is of absolutely no help. If you think of the set of all possible 4d6 drop the lowest characters as defining a multivariate "character space", can you create an algorithm that can eliminate parts of that space (worthless characters) from consideration for subsequent calculations? For instance, any character with three scores of 3 is "worthless," regardless of the other scores, so, you could just ignore all characters with three 3s and have that many fewer calculations to make. The only reason I'm suggesting this is that it sounds like a problem that biologists run into when trying to analyze evolutionary relationships. You have a matrix of organisms and scores for various traits, and you can create "trees" that are networks implying certain changes in traits, or steps. The tree with the fewest steps is considered to be best, so you can use a computer to find the tree with the fewest steps. That's easy for three organisms, for which there are only three possible combinations, but, as you increase the number of organisms in the analysis, the number of possible trees increases by a sort of factorial progression. Thus, looking at every possible tree becomes impractical in terms of time. One solution is an algorithm called "branch-and-bound", which basically finds the shortest tree by a process analogous to what I described above. I forget the details of how it works at the moment, but someone familiar with graph theory may know these things; apparently similar algorithms are used for telecommunications networks. --Axe [/QUOTE]

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