Fig. 1

An index building example. \(X_{i}\) represents a 32-mer extracted from reference genome. a, b, c, d are the keys calculated from \(X_{i}\). \(n_{i}\) represents the number of keys smaller than the corresponding key. For example, \(n_{1}\) is the number of keys smaller than a. Specifically, \(X_{1}\), \(X_{4}\) and \(X_{7}\) have the same key a. So there are \(n_{1} + 3\) keys smaller than \(a + 1\). Thus, \(l_{1}\), \(l_{2}\) and \(l_{3}\) indexed with \(n_{1}\), \(n_{1} + 1\), \(n_{1} + 2\) in value table are the locations for \(X_{1}\), \(X_{4}\) and \(X_{7}\)