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A metric index for approximate string matching. (English) Zbl 1087.68027
Summary: We present a radically new indexing approach for approximate string matching. The scheme uses the metric properties of the edit distance and can be applied to any other metric between strings. We build a metric space where the sites are the nodes of the suffix tree of the text, and the approximate query is seen as a proximity query on that metric space. This permits us finding the \(occ\) occurrences of a pattern of length \(m\), permitting up to \(r\) differences, in a text of length \(n\) over an alphabet of size \(\sigma\), in average time \(O(m^{1+ \varepsilon}+occ)\) for any \(\varepsilon>0\), if \(r=o(m/\log_\sigma m)\) and \(m>((1 +\varepsilon)/ \varepsilon)\log_\sigma n\). The index works well up to \(r<(3-\sqrt 2)m/ \log_\sigma m\), where it achieves its maximum average search complexity \(O(m^{1+\sqrt 2+\varepsilon}+occ)\). The construction time of the index is \(O(m^{1+ \sqrt 2+\varepsilon}n\log n)\) and its space is \(O(m^{1+\sqrt 2+\varepsilon}n)\). This is the first index achieving average search time polynomial in \(m\) and independent of \(n\), for \(r=O (m/\log_\sigma m)\). Previous methods achieve this complexity only for \(r=O(m/\log_\sigma n)\). We also present a simpler scheme needing \(O(n)\) space.

MSC:
68P10 Searching and sorting
Software:
GLIMPSE; PATRICIA
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