4,543 research outputs found
Efficient seeding techniques for protein similarity search
We apply the concept of subset seeds proposed in [1] to similarity search in
protein sequences. The main question studied is the design of efficient seed
alphabets to construct seeds with optimal sensitivity/selectivity trade-offs.
We propose several different design methods and use them to construct several
alphabets.We then perform an analysis of seeds built over those alphabet and
compare them with the standard Blastp seeding method [2,3], as well as with the
family of vector seeds proposed in [4]. While the formalism of subset seed is
less expressive (but less costly to implement) than the accumulative principle
used in Blastp and vector seeds, our seeds show a similar or even better
performance than Blastp on Bernoulli models of proteins compatible with the
common BLOSUM62 matrix
Efficient seeding techniques for protein similarity search
We apply the concept of subset seeds proposed in [1] to similarity search in
protein sequences. The main question studied is the design of efficient seed
alphabets to construct seeds with optimal sensitivity/selectivity trade-offs.
We propose several different design methods and use them to construct several
alphabets.We then perform an analysis of seeds built over those alphabet and
compare them with the standard Blastp seeding method [2,3], as well as with the
family of vector seeds proposed in [4]. While the formalism of subset seed is
less expressive (but less costly to implement) than the accumulative principle
used in Blastp and vector seeds, our seeds show a similar or even better
performance than Blastp on Bernoulli models of proteins compatible with the
common BLOSUM62 matrix
Longest common substring with approximately k mismatches
In the longest common substring problem we are given two strings of length n and must find a substring of maximal length that occurs in both strings. It is well-known that the problem can be solved in linear time, but the solution is not robust and can vary greatly when the input strings are changed even by one letter. To circumvent this, Leimester and Morgenstern introduced the problem of the longest common substring with k mismatches. Lately, this problem has received a lot of attention in the literature, and several algorithms have been suggested. The running time of these algorithms is n^{2-o(1)}, and unfortunately, conditional lower bounds have been shown which imply that there is little hope to improve this bound.
In this paper we study a different but closely related problem of the longest common substring with approximately k mismatches and use computational geometry techniques to show that it admits a randomised solution with strongly subquadratic running time
The streaming -mismatch problem
We consider the streaming complexity of a fundamental task in approximate
pattern matching: the -mismatch problem. It asks to compute Hamming
distances between a pattern of length and all length- substrings of a
text for which the Hamming distance does not exceed a given threshold . In
our problem formulation, we report not only the Hamming distance but also, on
demand, the full \emph{mismatch information}, that is the list of mismatched
pairs of symbols and their indices. The twin challenges of streaming pattern
matching derive from the need both to achieve small working space and also to
guarantee that every arriving input symbol is processed quickly.
We present a streaming algorithm for the -mismatch problem which uses
bits of space and spends \ourcomplexity time on
each symbol of the input stream, which consists of the pattern followed by the
text. The running time almost matches the classic offline solution and the
space usage is within a logarithmic factor of optimal.
Our new algorithm therefore effectively resolves and also extends an open
problem first posed in FOCS'09. En route to this solution, we also give a
deterministic -bit encoding of all
the alignments with Hamming distance at most of a length- pattern within
a text of length . This secondary result provides an optimal solution to
a natural communication complexity problem which may be of independent
interest.Comment: 27 page
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