Consider a website containing a collection of webpages with data such as in Yahoo or the Open Directory project. Each page is associated with a weight representing the frequency with which that page is accessed by users. In the tree hierarchy representation, accessing each page requires the user to travel along the path leading to it from the root. By enhancing the index tree with additional edges (hotlinks) one may reduce the access cost of the system. In other words, the hotlinks reduce the expected number of steps needed to reach a leaf page from the tree root, assuming that the user knows which hotlinks to take. The hotlink enhancement problem involves finding a set of hotlinks minimizing this cost. This article proposes the first exact algorithm for the hotlink enhancement problem. This algorithm runs in polynomial time for trees with logarithmic depth. Experiments conducted with real data show that significant improvement in the expected number of accesses per search can be achieved in websites using this algorithm. These experiments also suggest that the simple and much faster heuristic proposed previously by Czyzowicz et al. [2003] creates hotlinks that are nearly optimal in the time savings they provide to the user. The version of the hotlink enhancement problem in which the weight distribution on the leaves is unknown is discussed as well. We present a polynomial-time algorithm that is optimal for any tree for any depth.

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Let A be a sequence of n ≥ 0 real numbers. A subsequence of A is a sequence of contiguous elements of A. A maximum scoring subsequence of A is a subsequence with largest sum of its elements , which can be found in O(n) time by Kadane's dynamic programming algorithm. We consider in this paper two problems involving maximal scoring subsequences of a sequence. Both of these problems arise in the context of buffer memory minimization in computer networks. The first one, which is called INSERTION IN A SEQUENCE WITH SCORES (ISS), consists in inserting a given real number x in A in such a way to minimize the sum of a maximum scoring subsequence of the resulting sequence, which can be easily done in O(n 2 ) time by successively applying Kadane's algorithm to compute the maximum scoring subsequence of the resulting sequence corresponding to each possible insertion position for x. We show in this paper that the ISS problem can be solved in linear time and space with a more specialized algorithm. The second problem we consider in this paper is the SORTING A SEQUENCE BY SCORES (SSS) one, stated as follows: find a permutation A ′ of A that minimizes the sum of a maximum scoring subsequence. We show that the SSS problem is strongly NP-Hard and give a 2-approximation algorithm for it. * This work is partially supported by FUNCAP/INRIA (Ceará State, Brazil/France) and CNPq (Brazil) research projects. A slightly different version of this paper has been submitted for journal publication. † Partially supported by a doctoral scholarship of CAPES (Programa de Demanda Social). ‡ http://www.lia.ufc.br/˜pargo § Partially supported by a FUNCAP grant.