Efficient Algorithms for the Hotlink Assignment Problem: The Worst Case Search

Let T be a rooted directed tree where nodes represent web pages of a web site and arcs represent hyperlinks. In this case, when a user searches for an information i, it traverses a directed path in T, from the root node to the node that contains i. In this context, hotlinks are defined as additional hyperlinks added to web pages in order to reduce the number of accessed pages per search. In this paper, we address the problem of inserting at most 1 hotlink in each web page, so as to minimize the number of accesses in a worst case search. We present a (14/3)-approximate algorithm that runs in a O(n log m) time and requires a linear space, where n and m are the number of nodes (internal and external) and the number of leaves in T, respectively. We also introduce an exact dynamic programming algorithm which runs in O(n(nm)2.284) time and uses O(n(nm)1.441) space. By extending the techniques presented here, a polynomial time algorithm can also be obtained when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal K}=O(1)$\end{document} hotlinks may be inserted in each page. The best known result for this problem is a polytime algorithm with constant approximation ratio for trees with bounded degree presented by Gerstel et. al. [1].