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 w 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 1.141 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 l of at most \(\frac{2H(p)}{\log (k+1)}\) and \(\frac{H(p)}{\log (k+d) -- \log d}\), respectively. Finally, we present an algorithm implementing these methods in O(n logn) time, an improvement over the previous O(n 2) time algorithms.
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Douïeb, K., Langerman, S. (2006). Near-Entropy Hotlink Assignments. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_28
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DOI: https://doi.org/10.1007/11841036_28
Publisher Name: Springer, Berlin, Heidelberg
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