Near-Entropy Hotlink Assignments

Abstract

Consider a rooted tree T of arbitrary maximum degree d representing a collection of n web pages connected via a set of links, all reachable from a source home page represented by the root of T. Each web page i carries a weight wi representative of the frequency with which it is visited. By adding hotlinks - shortcuts from a node to one of its descendents - we wish to minimize the expected number of steps / needed to visit pages from the home page, expressed as a function of the entropy H(p) of the access probabilities p. This paper introduces several new strategies for effectively assigning hotlinks in a tree. For assigning exactly one hotlink per node, our method guarantees an upper bound on / of 1.141 H(p)+1 if d>2 and 1.08 H (p) + 2/3 if d=2. We also present the first efficient general methods for assigning at most k hotlinks per node in trees of arbitrary maximum degree, achieving bounds on / of at most 2H(p)/log(k+1) and H(p)/log(k+d-logd, respectively. Finally, we present an algorithm implementing these methods in O(n logn) time, an improvement over the previous O(n2) time algorithms.