par Douieb, Karim 
;Langerman, Stefan
Référence Algorithmica, 58, 2, page (221-244)
Publication Publié, 2010
;Langerman, Stefan Référence Algorithmica, 58, 2, page (221-244)
Publication Publié, 2010
Article révisé par les pairs
| Résumé : | 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 probability p i 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 l 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 l of 1.141H(p)+1 if d>2 and 1.08H(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 l of at most {2H(p)}/{\log(k+1)}+1 and {H(p)}/{\log(k+d)-\log d}+1, respectively. All our methods are strong, i.e.; they provide the same guarantees on all subtrees after the assignment. We also present an algorithm implementing these methods in O(nlog∈n) time, an improvement over the previous O(n 2) time algorithms. Finally we prove a Ω(nlog∈n) lower bound on the running time of any strong method that guarantee an average access time strictly better than 2H(p). © 2008 Springer Science+Business Media, LLC. |
