I agree there is a risk of misinterpretation as in "all kind all linked lists have been patented, here is the patent" and for this reason, it maybe would have been better to get an even more precise title. By i'm technically still fine with the current one. The claims (both in the application and in the granted patent) barely talk about traversing the "primary" or the "auxiliary" list which provide another sequence (well, providing the same would be... useless), not any kind of tricky algorithm like efficient multiple simultaneous sorting or i don't know what, not even a plain and boring insertion is covered!
This is a special case of traversing multiple linked lists, which is a basic technique. I actually even hesitate to say it is a technique, or at least to distinguish this technique from the very same technique of using a single linked list, because I don't think I could ever come up with a plausible justification for why anybody previously knowing how to use one would not be able to use two.
The restriction making this a special case is that all lists contain the same set of elements. Given the claims, that restriction is unnecessarily narrow and have no technical effect. So the only thing that distinguish this patent from a patent on a particular (but still 100% basic) use of single linked lists, is the phrasing, and the empty (still given the context) emphasis on the fact there are not one, but two, or even three lists.
So despite the fact that basic singly-linked lists + limited to one list by element would not be covered by this patent even in the parallel universe where it would be considered valid (and while we can note that on the contrary, prev/next linked list would), given that it only claims (with many more sentences) that if you have two lists, you can traverse one, or you can traverse the other, i will continue to argue that it covers linked lists, maybe under certain conditions, all right, but those conditions are insufficient to mandate the precision that this is a modification of linked lists, because it is not a modification, it is just about the basic traversal of multiple plain classical linked lists.
(Also, one a side note, I found it cute how the claims are structured, like if the author thought there was a possibility that prior art could be found for two pointers but not three.)
Edit: About the inflammatory part, it might as well have been even more inflammatory by being even more descriptive. Somebody has patented traversal of linked lists.
Imagine the headline read, "Gas up to $8.23 a gallon" and only upon reading the article did you discover that the "gas" they're talking about is 110 octane race gas. Yes, race gas is a type of gas(oline), but the headline is still quite misleading, as the common definition, without qualifiers, is the pump variety.
As for claims of the patent, it does really cover traversing at all. It mentions it, but the meat of the patent is the data structure having two or three pointers built in for traversing and choosing between those pointers for different traversals. This is all very obvious and frivolous, but it's not claiming the basics of traversing a linked list.
(As for your side note, I found that really strange as well. I can't imagine why thy specifically called out the cases of 2 and 3 pointers. Were they planning on filing later for 4 and 5 when they figured it out?)
I argue that it's claiming the traversal of linked lists, provided you have a choice between at least two linked lists containing the same set of elements. I argue that this restriction is meaningless, because it has no technical impact in this patent. Even when the patent seems to try to be a little more broad, by trying to describe the data structure itself, this description also depends on traversal and nothing else: "[claim 1 ...] said primary function pointer functioning as a primary linked list to direct a computer program to a first sequence to _traverse_ said computerized list [...]" (x2 because the same thing is written for the "auxiliary" list, then x3 in claim 2 for the "tertiary" one).
There is never any interaction described between one list and the other -- so from the point of view of patenting I don't see anything difference between this patent and a mere description of basic single linked lists, description centered on its traversal (the various enumerations are to be considered as irrelevant in themselves, and are not supplemented by anything else).
That reason alone would be one of the major angle of attack of the patent, would it not be already even more basically invalid because of triviality and prior art. The only challenge would be to present those formal concepts using casual language clearly enough so that nobody would mistake this description as the description of a new structure (even in the hypothetical alternate universe where nobody ever previously used two lists at a times for ordering the same sets of elements)
This is a special case of traversing multiple linked lists, which is a basic technique. I actually even hesitate to say it is a technique, or at least to distinguish this technique from the very same technique of using a single linked list, because I don't think I could ever come up with a plausible justification for why anybody previously knowing how to use one would not be able to use two. The restriction making this a special case is that all lists contain the same set of elements. Given the claims, that restriction is unnecessarily narrow and have no technical effect. So the only thing that distinguish this patent from a patent on a particular (but still 100% basic) use of single linked lists, is the phrasing, and the empty (still given the context) emphasis on the fact there are not one, but two, or even three lists.
So despite the fact that basic singly-linked lists + limited to one list by element would not be covered by this patent even in the parallel universe where it would be considered valid (and while we can note that on the contrary, prev/next linked list would), given that it only claims (with many more sentences) that if you have two lists, you can traverse one, or you can traverse the other, i will continue to argue that it covers linked lists, maybe under certain conditions, all right, but those conditions are insufficient to mandate the precision that this is a modification of linked lists, because it is not a modification, it is just about the basic traversal of multiple plain classical linked lists.
(Also, one a side note, I found it cute how the claims are structured, like if the author thought there was a possibility that prior art could be found for two pointers but not three.)
Edit: About the inflammatory part, it might as well have been even more inflammatory by being even more descriptive. Somebody has patented traversal of linked lists.