Abstract
Vector algorithms allow the computation of an output vector r = r1 r2 ⋯ rm given an input vector e = e1 e2 ⋯ em in a bounded number of operations, independent of m the length of the vectors. The allowable operations are usually restricted to bit-wise operations available in processors, including shifts and binary addition with carry. These restrictions imple that the existence of a vector algorithm for a particular problem opens the way to extremely fast implementations, using the inherent parallelism of bit-wise operations. This paper presents general results on the existence and construction of vertor algorithms, with a particular focus on problems arising from computational biology. We show that efficient vector algorithms exist for the problem of approximate string matching with arbitrary weighted distances, generalizing a previous result by G. Myers. We also characterize a class of automata for which vector algorithms can be automatically derived from the transition table of the automata.
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