Martin Farach

Optimal suffix tree construction with large alphabets

The su x tree of a string is the fundamental data structure of combinatorial pattern matching. In this paper, we present a novel, deterministic algorithm for the construction of su x trees. We settle the main open problem in the construction of su x trees: we build su x trees in linear time for integer alphabet.The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. Weiner (1973), who introduced the data structure, gave an O(n)-time algorithm for building the suffix tree of an n-character string drawn from a constant size alphabet. In the comparison model, there is a trivial /spl Omega/(n log n)-time lower bound based on sorting, and Weiners algorithm matches this bound trivially. For integer alphabets, a substantial gap remains between the known upper and lower bounds, and closing this gap is the main open question in the construction of suffix trees. There is no super-linear lower bound, and the fastest known algorithm was the O(n log n) time comparison based algorithm. We settle this open problem by closing the gap: we build suffix trees in linear time for integer alphabet.

On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)

We consider the problem of fitting an n × n distance matrix D by a tree metric T. Let

On the agreement of many trees

\varepsilon

Local rules for protein folding on a triangular lattice and generalized hydrophobicity in the HP model.

be the distance to the closest tree metric under the

Alphabet dependence in parameterized matching

L_{\infty}

Optimal superprimitivity testing for strings

norm; that is,

Efficient 2-Dimensional Approximate Matching of Half-Rectangular Figures

\varepsilon=\min_T\{\parallel T-D\parallel{\infty}\}

An Alphabet Independent Approach to Two-Dimensional Pattern Matching

. First we present an O(n2) algorithm for finding a tree metric T such that

Group testing problems with sequences in experimental molecular biology

\parallel T-D\parallel{\infty}\leq 3\varepsilon

Adaptive dictionary matching

. Second we show that it is