Approximate Hotlink Assignment

  • Authors:
  • Evangelos Kranakis;Danny Krizanc;Sunil Shende

  • Affiliations:
  • Carleton University, School of Computer Science, Ottawa, Canada K1S 5B6;Department of Mathematics, Wesleyan University, Middletown, USA 06459;Department of Computer Science, Rutgers University, Camden, USA 08102

  • Venue:
  • ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
  • Year:
  • 2009

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Abstract

Consider a directed rooted tree T = (V,E) of maximal degree d representing a collection V of web pages connected via a set E of links all reachable from a source home page, represented by the root of T. Each leaf web page carries a weight representative of the frequency with which it is visited. By adding hotlinks, shortcuts from a node to one of its descendents, we are interested in minimizing the expected number of steps needed to visit the leaf pages from the home page. We give an O(N 2) time algorithm for assigning hotlinks so that the expected number of steps to reach the leaves from the root of the tree is at most $$\tfrac{{H\left( p \right)}}{{log\left( {d + 1} \right) - \left( {d/\left( {d + 1} \right)} \right)log d}} + \tfrac{{d + 1}}{d}$$, where H(p) is the entropy of the probability (frequency) distribution p =p1,p2, , . . . , pN on the N leaves of the given tree, i.e., pi is the weight on the ith leaf. The best known lower bound for this problem is $$\tfrac{{H\left( p \right)}}{{log\left( {d + 1} \right)}}$$. Thus our algorithm approximates the optimal hotlink assignment to within a constant for any fixed d.