Alberto Apostolico

The Myriad Virtues of Subword Trees

Several nontrivial applications of subword trees have been developed since their first appearance. Some such applications depart considerably from the original motivations. A brief account of them is attempted here.

Optimal off-line detection of repetitions in a string

An algorithm is presented to detect—within optimal time O(n log n) and space O(n), off-line on a RAM—all of the distinct repetitions in a given textstring on a finite alphabet. The proposed strategy is self-contained, as it depends more heavily on algorithmic design considerations than on the combinatorial properties of the output. It is based on a new data structure, the leaf-tree, which is particularly suited to exploit simple properties of the suffix tree associated with the string to be analyzed.

The longest common subsequence problem revisited

This paper re-examines, in a unified framework, two classic approaches to the problem of finding a longest common subsequence (LCS) of two strings, and proposes faster implementations for both. Letl be the length of an LCS between two strings of lengthm andn ≥m, respectively, and let s be the alphabet size. The first revised strategy follows the paradigm of a previousO(ln) time algorithm by Hirschberg. The new version can be implemented in timeO(lm · min logs, logm, log(2n/m)), which is profitable when the input strings differ considerably in size (a looser bound for both versions isO(mn)). The second strategy improves on the Hunt-Szymanski algorithm. This latter takes timeO((r +n) logn), wherer≤mn is the total number of matches between the two input strings. Such a performance is quite good (O(n logn)) whenr∼n, but it degrades to Θ(mn logn) in the worst case. On the other hand the variation presented here is never worse than linear-time in the productmn. The exact time bound derived for this second algorithm isO(m logn +d log(2mn/d)), whered ≤r is the number ofdominant matches (elsewhere referred to asminimal candidates) between the two strings. Both algorithms require anO(n logs) preprocessing that is nearly standard for the LCS problem, and they make use of simple and handy auxiliary data structures.

Efficient parallel algorithms for string editing and related problems

The string editing problem for input strings x and y consists of transforming x into y by performing a series of weighted edit operations on x of overall minimum cost. An edit operation on x can be the deletion of a symbol from x, the insertion of a symbol in x or the substitution of a symbol of x with another symbol. This problem has a well-known

Parallel construction of a suffix tree with applications

O(|x||y|)

The Boyer Moore Galil string searching strategies revisited

time-sequential solution. Efficient PRAM parallel algorithms for the string editing problem are given. If

Efficient Detection of Unusual Words

m = \min (|x|,|y|)

Efficient detection of quasiperiodicities in strings

and

Optimal superprimitivity testing for strings

n = \max (|x|,|y|)

Monotony of surprise and large-scale quest for unusual words

, then the CREW bound is