Algorithmic Complexity of Protein Identification: Combinatorics of Weighted Strings | |

Authors: | Mark Cieliebak, Thomas Erlebach, Zsuzsanna Lipták, Jens Stoye, and Emo Welzl |

Reference: | Discrete
Applied Mathematics (DAM). Vol 137, No. 1, pp. 27-46, 2004. |

Download: | Postscript (.ps) or PDF (.pdf) or compressed (.zip) |

Abstract: |
We investigate a problem which arises in computational
biology: Given a constant--size alphabet
A with a weight function
$\mu: A --> N$, find an efficient data structure
and query algorithm solving the following problem: For a string $\sigma$
over A and a weight $M \in N$, decide
whether $\sigma$ contains a substring with weight M, where the
weight of a string is the sum of the weights of its letters (Mass Finding
Problem). If the answer is yes, then we may in addition require a witness,
i.e., indices $i \leq j$ such that the substring beginning
at position i and ending at position j has weight M.
We allow preprocessing of the string, and measure efficiency in two parameters:
storage space required for the preprocessed data, and running time of
the query algorithm for given M. We are interested in data structures
and algorithms requiring subquadratic storage space and sublinear query
time, where we measure the input size as the length n of the
input string $\sigma$. Among others, we present two non-trivial efficient
algorithms: LOOKUP solves the problem with O(n) storage space
and $O(\frac{n}{\log n})$ time; INTERVAL solves the
problem for binary alphabets with O(n) storage space in O(log
n) query time. We introduce other variants of the problem and
sketch how our algorithms may be extended for these variants. Finally,
we discuss combinatorial properties of weighted strings. |

Remarks: |

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