12,739 research outputs found
An Elegant Algorithm for the Construction of Suffix Arrays
The suffix array is a data structure that finds numerous applications in
string processing problems for both linguistic texts and biological data. It
has been introduced as a memory efficient alternative for suffix trees. The
suffix array consists of the sorted suffixes of a string. There are several
linear time suffix array construction algorithms (SACAs) known in the
literature. However, one of the fastest algorithms in practice has a worst case
run time of . The problem of designing practically and theoretically
efficient techniques remains open. In this paper we present an elegant
algorithm for suffix array construction which takes linear time with high
probability; the probability is on the space of all possible inputs. Our
algorithm is one of the simplest of the known SACAs and it opens up a new
dimension of suffix array construction that has not been explored until now.
Our algorithm is easily parallelizable. We offer parallel implementations on
various parallel models of computing. We prove a lemma on the -mers of a
random string which might find independent applications. We also present
another algorithm that utilizes the above algorithm. This algorithm is called
RadixSA and has a worst case run time of . RadixSA introduces an
idea that may find independent applications as a speedup technique for other
SACAs. An empirical comparison of RadixSA with other algorithms on various
datasets reveals that our algorithm is one of the fastest algorithms to date.
The C++ source code is freely available at
http://www.engr.uconn.edu/~man09004/radixSA.zi
Deterministic sub-linear space LCE data structures with efficient construction
Given a string of symbols, a longest common extension query
asks for the length of the longest common prefix of the
th and th suffixes of . LCE queries have several important
applications in string processing, perhaps most notably to suffix sorting.
Recently, Bille et al. (J. Discrete Algorithms 25:42-50, 2014, Proc. CPM 2015:
65-76) described several data structures for answering LCE queries that offers
a space-time trade-off between data structure size and query time. In
particular, for a parameter , their best deterministic
solution is a data structure of size which allows LCE queries to be
answered in time. However, the construction time for all
deterministic versions of their data structure is quadratic in . In this
paper, we propose a deterministic solution that achieves a similar space-time
trade-off of query time using
space, but significantly improve the construction time to
.Comment: updated titl
Lyndon Array Construction during Burrows-Wheeler Inversion
In this paper we present an algorithm to compute the Lyndon array of a string
of length as a byproduct of the inversion of the Burrows-Wheeler
transform of . Our algorithm runs in linear time using only a stack in
addition to the data structures used for Burrows-Wheeler inversion. We compare
our algorithm with two other linear-time algorithms for Lyndon array
construction and show that computing the Burrows-Wheeler transform and then
constructing the Lyndon array is competitive compared to the known approaches.
We also propose a new balanced parenthesis representation for the Lyndon array
that uses bits of space and supports constant time access. This
representation can be built in linear time using words of space, or in
time using asymptotically the same space as
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