binary search to find the highest lower element or the lowest higher element. then insert your new value in the location. one problem with that is insertion takes a lot of time. but you can migitage that using the spaced library sort. but then you add time by having to compare to blank slots, but you can fix that by having each item contain a link to the next item that's not blank. another option might be to have only a linked list, but then we have to figure out how to jump to the middle of two values. i believe we can do that; every time we insert an item, link the last mid-point we came to before it to that item as its middle value. actually each item should have the value of hwich element it is in the list, and pointers to both its parent pivots. and then if the element is closer to half way between the two parents than its parents half way child then it replaces its parents half way child with itself. the parents of the first pivot are considered the two end values.