A Metric Index for Approximate String Matching

Edgar Chávez and Gonzalo Navarro

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 R occurrences of a pattern of length m in a text of length n in average time O(m\log^2 n + m^2 + R), using O(n\log n) space and O(n\log^2 n) index construction time. This complexity improves by far over all other previous methods. We also show a simpler scheme needing O(n) space.