4,036 research outputs found
On the maximal sum of exponents of runs in a string
A run is an inclusion maximal occurrence in a string (as a subinterval) of a
repetition with a period such that . The exponent of a run
is defined as and is . We show new bounds on the maximal sum of
exponents of runs in a string of length . Our upper bound of is
better than the best previously known proven bound of by Crochemore &
Ilie (2008). The lower bound of , obtained using a family of binary
words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the
maximal sum of exponents of runs in a string of length is smaller than Comment: 7 pages, 1 figur
Understanding maximal repetitions in strings
The cornerstone of any algorithm computing all repetitions in a string of
length n in O(n) time is the fact that the number of runs (or maximal
repetitions) is O(n). We give a simple proof of this result. As a consequence
of our approach, the stronger result concerning the linearity of the sum of
exponents of all runs follows easily
Lempel-Ziv Factorization May Be Harder Than Computing All Runs
The complexity of computing the Lempel-Ziv factorization and the set of all
runs (= maximal repetitions) is studied in the decision tree model of
computation over ordered alphabet. It is known that both these problems can be
solved by RAM algorithms in time, where is the length of
the input string and is the number of distinct letters in it. We prove
an lower bound on the number of comparisons required to
construct the Lempel-Ziv factorization and thereby conclude that a popular
technique of computation of runs using the Lempel-Ziv factorization cannot
achieve an time bound. In contrast with this, we exhibit an
decision tree algorithm finding all runs in a string. Therefore, in the
decision tree model the runs problem is easier than the Lempel-Ziv
factorization. Thus we support the conjecture that there is a linear RAM
algorithm finding all runs.Comment: 12 pages, 3 figures, submitte
A Faster Implementation of Online Run-Length Burrows-Wheeler Transform
Run-length encoding Burrows-Wheeler Transformed strings, resulting in
Run-Length BWT (RLBWT), is a powerful tool for processing highly repetitive
strings. We propose a new algorithm for online RLBWT working in run-compressed
space, which runs in time and bits of space, where
is the length of input string received so far and is the number of runs
in the BWT of the reversed . We improve the state-of-the-art algorithm for
online RLBWT in terms of empirical construction time. Adopting the dynamic list
for maintaining a total order, we can replace rank queries in a dynamic wavelet
tree on a run-length compressed string by the direct comparison of labels in a
dynamic list. The empirical result for various benchmarks show the efficiency
of our algorithm, especially for highly repetitive strings.Comment: In Proc. IWOCA201
Two Ising Models Coupled to 2-Dimensional Gravity
To investigate the properties of matter coupled to d{--}gravity we
have performed large-scale simulations of two copies of the Ising Model on a
dynamical lattice. We measure spin susceptibility and percolation critical
exponents using finite-size scaling. We show explicitly how logarithmic
corrections are needed for a proper comparison with theoretical exponents. We
also exhibit correlations, mediated by gravity, between the energy and magnetic
properties of the two Ising species. The prospects for extending this work
beyond are addressed.Comment: revised version w/ typos corrected; standard latex w/ epsf and 9
figure
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