Information distributed through the Web keeps growing faster day by day, and for this reason, several techniques for extracting Web data have been suggested during last years. Often, extraction tasks are performed through so called wrappers, procedures extracting information from Web pages, e.g. implementing logic-based techniques. Many fields of application today require a strong degree of robustness of wrappers, in order not to compromise assets of information or reliability of data extracted.
Theoretical background on techniques and algorithms widely adopted in this work relies on several Computer Science and Applied Mathematics fields such as Algorithms and Data Structures and Artificial Intelligence. In the setting of Web data extraction, especially algorithms on (DOM) trees play a predominant role. Approaches to analyze similarities between trees were developed starting from the well-known problem of finding the longest common subsequence(s) between two strings. Several algorithms were suggested, for example Hirshberg @cite_1 provided the proof of correctness of three of them.
@cite_1
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The main issue for effective Web information extraction is how to recognize similar patterns in a Web page. Traditionally, it has been shown that pattern matching by using the HTML DOM tree is more efficient than the simple string matching approach. Nonetheless, previous tree-based pattern matching methods have problems by assuming that all HTML tags have the same values, assigning the same weight to each node in HTML trees. This paper proposes an enhanced tree matching algorithm that improves the tree edit distance method by considering the characteristics of HTML features. We assign different values to different HTML tree nodes according to their weights for displaying the corresponding data objects in the browser. Pattern matching of HTML patterns is done by obtaining the maximum mapping values of two HTML trees that are constructed with weighted node values from HTML data objects. Experiments are done over several Web commerce sites to evaluate the effectiveness of the proposed HTML tree matching algorithm. The problem of finding a longest common subsequence of two strings is discussed. This problem arises in data processing applications such as comparing two files and in genetic applications such as studying molecular evolution. The difficulty of computing a longest common subsequence of two strings is examined using the decision tree model of computation, in which vertices represent “equal - unequal” comparisons. It is shown that unless a bound on the total number of distinct symbols is assumed, every solution to the problem can consume an amount of time that is proportional to the product of the lengths of the two strings. A general lower bound as a function of the ratio of alphabet size to string length is derived. The case where comparisons between symbols of the same string are forbidden is also considered and it is shown that this problem is of linear complexity for a two-symbol alphabet and quadratic for an alphabet of three or more symbols. This paper presents a new web mining scheme for parallel data acquisition. Based on the Document Object Model (DOM), a web page is represented as a DOM tree. Then a DOM tree alignment model is proposed to identify the translationally equivalent texts and hyperlinks between two parallel DOM trees. By tracing the identified parallel hyperlinks, parallel web documents are recursively mined. Compared with previous mining schemes, the benchmarks show that this new mining scheme improves the mining coverage, reduces mining bandwidth, and enhances the quality of mined parallel sentences. Given dissimilarity data on pairs of objects in a set, we study the problem of fitting a tree metric to this data so as to minimize additive error (i.e. some measure of the difference between the tree metric and the given data). This problem arises in constructing an M-level hierarchical clustering of objects (or an ultrametric on objects) so as to match the given dissimilarity data - a basic problem in statistics. Viewed in this way, the problem is a generalization of the correlation clustering problem (which corresponds to M = 1). We give a very simple randomized combinatorial algorithm for the M-level hierarchical clustering problem that achieves an approximation ratio of M+2. This is a generalization of a previous factor 3 algorithm for correlation clustering on complete graphs. The problem of fitting tree metrics also arises in phylogeny where the objective is to learn the evolution tree by fitting a tree to dissimilarity data on taxa. The quality of the fit is measured by taking the l sub p norm of the difference between the tree metric constructed and the given data. Previous results obtained a factor 3 approximation for finding the closest tree tree metric under the l spl infin norm. No nontrivial approximation for general l sub p norms was known before. We present a novel LP formulation for this problem and obtain an O((log n log log n) sup 1 p ) approximation using this. Enroute, we obtain an O((log n log log n) sup 1 p ) approximation for the closest ultrametric under the l sub p norm. Our techniques are based on representing and viewing an ultrametric as a hierarchy of clusterings, and may be useful in other contexts.