Optimal multi-page navigation
I have come across many websites and even desktop applications that have a crumb control for navigating through pages of information.
For example, given X pages where the user is currently on page N, SOFU has a crumb control that represents page navigation as:
(X[N-1])(X[0])...(X[N-2])(X[N-1])(X[N])(X[N+1])(X[N+2])...(X[X-1])(X[N+1])
I've seen all sorts of variations of this control. I am wondering if there is a way to optimize this type of control so that the user can navigate to any data page with the minimum number of clicks. I know there are obvious answers, such as allowing the user to specify a page number or enter a URL, but I'm thinking of a more academic solution where no alternatives are available.
I am not very bright and suck on math. Any ideas where to even start without roughly forcing a solution?
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You can add links for pages in the fibonacci sequence from the current page to the beginning and end of the sequence, for example:
(X [0]) ... (X [N-8]) ... (X [N-5]) ... (X [N-3]) (X [N-2]) (X [ N-1]) (X [N]) (X [N + 1]) (X [N + 2]) (X [3]) ... (X [N + 5]) ... (X [ N + 8]) ... (X [X-1])
I think this will give you a good ratio of space references, but it will still take up a lot of space. If that's not good enough, you should think about how exactly your users know the page you're looking for and how many page links you can offer / tolerate.