2.1 Wilber's 2nd Lower Bound

Let 〈x1, x2, ..., xm〉 be the access sequence. For each access xj compute the following Wilber number. We look at where xj fits among xi, xi+1, ..., xj−1 for all i = j−1, j−2... that is, counting backwards from j − 1 until the previous access to the key xj. Now, we say that ai < xj < bi, where ai and bi are the tightest bounds on xj discovered so far. Each time i is decremented, either ai increases or bi decreases (more tightly fitting xj), or nothing happens (the access is uninteresting for xj). The Wilber number is the number of alternations between ai increasing and bi decreasing.