Graphs and algorithms
Boyer-Moore approach to approximate string matching (extended abstract)
SWAT '90 Proceedings of the second Scandinavian workshop on Algorithm theory
A new approach to text searching
Communications of the ACM
Fast text searching: allowing errors
Communications of the ACM
Algorithms for computing finite semigroups
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
A fast string searching algorithm
Communications of the ACM
Fast and Practical Approximate String Matching
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Finite-state transducers in language and speech processing
Computational Linguistics
Max-plus algebra and discrete event simulation on parallel hierarchical heterogeneous platforms
Euro-Par 2010 Proceedings of the 2010 conference on Parallel processing
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The classical algorithms to align two biological sequences (Needleman and Wunsch and Smith and Waterman algorithms) can be seen as a sequence of elementary operations in (max, +) algebra: each line (viewed as a vector) of the dynamic programming table of the alignment algorithms can be deduced by a (max, +) multiplication of the previous line by a matrix. Taking into account the properties of these matrices there are only a finite number of nonproportional vectors. The use of this algebra allows one to imagine a faster equivalent algorithm. One can construct an automaton and afterwards skim through the sequence databank with this automaton in linear time. Unfortunately, the size of the automaton prevents using this approach for comparing global proteins. However, biologists frequently face the problem of comparing one short string against many others sequences. In that case this automaton version of dynamic programming results in a new algorithm which works faster than the classical algorithm.