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We present the first space and time optimal parallel algorithm for the pairwise sequence alignment problem, a fundamental problem in computational biology. This problem can be solved sequentially in O(mn) time and O(m+n) space, where m and n are the lengths of the sequences to be aligned. The fastest known parallel space-optimal algorithm for pairwise sequence alignment takes optimal O(m+n/p) space, but suboptimal O((m+n)2/p) time, where p is the number of processors. On the other hand, the most space economical time-optimal parallel algorithm takes O(mn/p) time, but O(m+n/p) space. We close this gap by presenting an algorithm that achieves both time and space optimality, i.e. requires only O((m+n)/p) space and O(mn/p) time. We also present an experimental evaluation of the proposed algorithm on an IBM xSeries cluster. Although presented in the context of full sequence alignments, our algorithm is applicable to other alignment problems in computational biology including local alignments and syntenic alignments. It is also a useful addition to the range of techniques available for parallel dynamic programming.