1,282 research outputs found
Algorithms to Compute the Lyndon Array
We first describe three algorithms for computing the Lyndon array that have
been suggested in the literature, but for which no structured exposition has
been given. Two of these algorithms execute in quadratic time in the worst
case, the third achieves linear time, but at the expense of prior computation
of both the suffix array and the inverse suffix array of x. We then go on to
describe two variants of a new algorithm that avoids prior computation of
global data structures and executes in worst-case n log n time. Experimental
evidence suggests that all but one of these five algorithms require only linear
execution time in practice, with the two new algorithms faster by a small
factor. We conjecture that there exists a fast and worst-case linear-time
algorithm to compute the Lyndon array that is also elementary (making no use of
global data structures such as the suffix array)
An Efficient generic algorithm for the generation of unlabelled cycles
In this report we combine two recent generation algorithms to obtain a
new algorithm for the generation of unlabelled cycles. Sawada's
algorithm lists all k-ary unlabelled cycles with fixed
content, that is, the
number of occurences of each symbol is fixed and given a priori.
The other algorithm, by the authors, generates all
multisets of objects with given total size n from any admissible
unlabelled class A. By admissible
we mean that the class can be specificied using atomic classes,
disjoints unions, products, sequences, (multi)sets, etc.
The resulting algorithm, which is the main contribution of this paper,
generates all cycles of objects with given total size n from any
admissible class A. Given the
generic nature of the algorithm, it is suitable for inclusion in
combinatorial libraries and for rapid prototyping. The new algorithm
incurs constant amortized time per generated cycle, the constant only
depending in the class A to which the objects in the cycle belong.Postprint (published version
Signal Identification In Discrete-Time Based On Internal-Model-Principle
This work presents an implementation of a signal identification algorithm which is based on the internal model principle. By using several internal models in feedback with a tuning function, this algorithm can decompose a signal into narrow-band signals and identify the frequencies, amplitudes and relative phases. A desired band-pass filter response can be achieved by selecting appropriate coefficients of the controllers and tuning functions, which can reject the noise and improve the performance. To achieve a result with fast transient characteristics, this system is then modified by adding a low-pass filter. This work is based on the previous work in continuous time. However, a discrete implementation should be much more practical. The simulation result shows a good tracking of the original signal with minimal response to measurement noise
Splitting and composition methods in the numerical integration of differential equations
We provide a comprehensive survey of splitting and composition methods for
the numerical integration of ordinary differential equations (ODEs). Splitting
methods constitute an appropriate choice when the vector field associated with
the ODE can be decomposed into several pieces and each of them is integrable.
This class of integrators are explicit, simple to implement and preserve
structural properties of the system. In consequence, they are specially useful
in geometric numerical integration. In addition, the numerical solution
obtained by splitting schemes can be seen as the exact solution to a perturbed
system of ODEs possessing the same geometric properties as the original system.
This backward error interpretation has direct implications for the qualitative
behavior of the numerical solution as well as for the error propagation along
time. Closely connected with splitting integrators are composition methods. We
analyze the order conditions required by a method to achieve a given order and
summarize the different families of schemes one can find in the literature.
Finally, we illustrate the main features of splitting and composition methods
on several numerical examples arising from applications.Comment: Review paper; 56 pages, 6 figures, 8 table
An adaptation reference-point-based multiobjective evolutionary algorithm
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics
Genericity of Filling Elements
An element of a finitely generated non-Abelian free group F(X) is said to be
filling if that element has positive translation length in every very small
action of F(X) on an -tree. We give a proof that the set of filling
elements of F(X) is exponentially F(X)-generic in the sense of Arzhantseva and
Ol'shanskii. We also provide an algebraic sufficient condition for an element
to be filling and show that there exists an exponentially F(X)-generic subset
of filling elements whose membership problem is solvable in linear time.Comment: 9 page
Efficient string algorithmics across alphabet realms
Stringology is a subfield of computer science dedicated to analyzing and processing sequences of symbols. It plays a crucial role in various applications, including lossless compression, information retrieval, natural language processing, and bioinformatics. Recent algorithms often assume that the strings to be processed are over polynomial integer alphabet, i.e., each symbol is an integer that is at most polynomial in the lengths of the strings. In contrast to that, the earlier days of stringology were shaped by the weaker comparison model, in which strings can only be accessed by mere equality comparisons of symbols, or (if the symbols are totally ordered) order comparisons of symbols. Nowadays, these flavors of the comparison model are respectively referred to as general unordered alphabet and general ordered alphabet. In this dissertation, we dive into the realm of both integer alphabets and general alphabets. We present new algorithms and lower bounds for classic problems, including Lempel-Ziv compression, computing the Lyndon array, and the detection of squares and runs. Our results show that, instead of only assuming the standard model of computation, it is important to also consider both weaker and stronger models. Particularly, we should not discard the older and weaker comparison-based models too quickly, as they are not only powerful theoretical tools, but also lead to fast and elegant practical solutions, even by today's standards
Delzant's T-invariant, Kolmogorov complexity and one-relator groups
We prove that ``almost generically'' for a one-relator group Delzant's
-invariant (which measures the smallest size of a finite presentation for a
group) is comparable in magnitude with the length of the defining relator. The
proof relies on our previous results regarding isomorphism rigidity of generic
one-relator groups and on the methods of the theory of Kolmogorov-Chaitin
complexity. We also give a precise asymptotic estimate (when is fixed and
goes to infinity) for the number of isomorphism classes of
-generator one-relator groups with a cyclically reduced defining relator of
length : Here
means that .Comment: A revised version, to appear in Comment. Math. Hel
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