Faster exon assembly by sparse spliced alignment

Assembling a gene from candidate exons is an important problem in computational biology. Among the most successful approaches to this problem is \emph{spliced alignment}, proposed by Gelfand et al., which scores different candidate exon chains within a DNA sequence of length $m$ by comparing them to a known related gene sequence of length n, $m = \Theta(n)$. Gelfand et al.\ gave an algorithm for spliced alignment running in time O(n^3). Kent et al.\ considered sparse spliced alignment, where the number of candidate exons is O(n), and proposed an algorithm for this problem running in time O(n^{2.5}). We improve on this result, by proposing an algorithm for sparse spliced alignment running in time O(n^{2.25}). Our approach is based on a new framework of \emph{quasi-local string comparison}.