289,397 research outputs found
Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings
We solve two inverse spectral problems for star graphs of Stieltjes strings
with Dirichlet and Neumann boundary conditions, respectively, at a selected
vertex called root. The root is either the central vertex or, in the more
challenging problem, a pendant vertex of the star graph. At all other pendant
vertices Dirichlet conditions are imposed; at the central vertex, at which a
mass may be placed, continuity and Kirchhoff conditions are assumed. We derive
conditions on two sets of real numbers to be the spectra of the above Dirichlet
and Neumann problems. Our solution for the inverse problems is constructive: we
establish algorithms to recover the mass distribution on the star graph (i.e.
the point masses and lengths of subintervals between them) from these two
spectra and from the lengths of the separate strings. If the root is a pendant
vertex, the two spectra uniquely determine the parameters on the main string
(i.e. the string incident to the root) if the length of the main string is
known. The mass distribution on the other edges need not be unique; the reason
for this is the non-uniqueness caused by the non-strict interlacing of the
given data in the case when the root is the central vertex. Finally, we relate
of our results to tree-patterned matrix inverse problems.Comment: 32 pages, 3 figure
K-Bit-Swap: a new operator for real-coded evolutionary algorithms
There have been a variety of crossover operators proposed for real-coded genetic algorithms (RCGAs). Such operators recombine values from pairs of strings to generate new solutions. In this article, we present a recombination operator for RCGAs that selects the string locations for change separately randomly in the parent and offspring, enabling solution parts to move within a string, and compare it to mainstream crossover operators in a set of experiments on a range of standard multidimensional optimization problems and a real-world clustering problem. We present two variants of the operator, either selecting bits uniformly at random in both strings or sampling the second bit from a normal distribution centered at the selected location in the first string. While the operator is biased toward exploitation of fitness space, the random selection of the second bit for swapping reduces this bias slightly. Statistical analysis of the experimental results using a nonparametric test shows the advantage of the new recombination operators on our test optimization functions
Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem
In the minimum common string partition (MCSP) problem two related input
strings are given. "Related" refers to the property that both strings consist
of the same set of letters appearing the same number of times in each of the
two strings. The MCSP seeks a minimum cardinality partitioning of one string
into non-overlapping substrings that is also a valid partitioning for the
second string. This problem has applications in bioinformatics e.g. in
analyzing related DNA or protein sequences. For strings with lengths less than
about 1000 letters, a previously published integer linear programming (ILP)
formulation yields, when solved with a state-of-the-art solver such as CPLEX,
satisfactory results. In this work, we propose a new, alternative ILP model
that is compared to the former one. While a polyhedral study shows the linear
programming relaxations of the two models to be equally strong, a comprehensive
experimental comparison using real-world as well as artificially created
benchmark instances indicates substantial computational advantages of the new
formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper
version replaces the one submitted on January 10, 2015, due to detected error
in the calculation of the variables involved in the ILP model
Scalability of Genetic Programming and Probabilistic Incremental Program Evolution
This paper discusses scalability of standard genetic programming (GP) and the
probabilistic incremental program evolution (PIPE). To investigate the need for
both effective mixing and linkage learning, two test problems are considered:
ORDER problem, which is rather easy for any recombination-based GP, and TRAP or
the deceptive trap problem, which requires the algorithm to learn interactions
among subsets of terminals. The scalability results show that both GP and PIPE
scale up polynomially with problem size on the simple ORDER problem, but they
both scale up exponentially on the deceptive problem. This indicates that while
standard recombination is sufficient when no interactions need to be
considered, for some problems linkage learning is necessary. These results are
in agreement with the lessons learned in the domain of binary-string genetic
algorithms (GAs). Furthermore, the paper investigates the effects of
introducing utnnecessary and irrelevant primitives on the performance of GP and
PIPE.Comment: Submitted to GECCO-200
Around Kolmogorov complexity: basic notions and results
Algorithmic information theory studies description complexity and randomness
and is now a well known field of theoretical computer science and mathematical
logic. There are several textbooks and monographs devoted to this theory where
one can find the detailed exposition of many difficult results as well as
historical references. However, it seems that a short survey of its basic
notions and main results relating these notions to each other, is missing.
This report attempts to fill this gap and covers the basic notions of
algorithmic information theory: Kolmogorov complexity (plain, conditional,
prefix), Solomonoff universal a priori probability, notions of randomness
(Martin-L\"of randomness, Mises--Church randomness), effective Hausdorff
dimension. We prove their basic properties (symmetry of information, connection
between a priori probability and prefix complexity, criterion of randomness in
terms of complexity, complexity characterization for effective dimension) and
show some applications (incompressibility method in computational complexity
theory, incompleteness theorems). It is based on the lecture notes of a course
at Uppsala University given by the author
Highly Scalable Algorithms for Robust String Barcoding
String barcoding is a recently introduced technique for genomic-based
identification of microorganisms. In this paper we describe the engineering of
highly scalable algorithms for robust string barcoding. Our methods enable
distinguisher selection based on whole genomic sequences of hundreds of
microorganisms of up to bacterial size on a well-equipped workstation, and can
be easily parallelized to further extend the applicability range to thousands
of bacterial size genomes. Experimental results on both randomly generated and
NCBI genomic data show that whole-genome based selection results in a number of
distinguishers nearly matching the information theoretic lower bounds for the
problem
Optimality program in segment and string graphs
Planar graphs are known to allow subexponential algorithms running in time
or for most of the paradigmatic
problems, while the brute-force time is very likely to be
asymptotically best on general graphs. Intrigued by an algorithm packing curves
in by Fox and Pach [SODA'11], we investigate which
problems have subexponential algorithms on the intersection graphs of curves
(string graphs) or segments (segment intersection graphs) and which problems
have no such algorithms under the ETH (Exponential Time Hypothesis). Among our
results, we show that, quite surprisingly, 3-Coloring can also be solved in
time on string graphs while an algorithm running
in time for 4-Coloring even on axis-parallel segments (of unbounded
length) would disprove the ETH. For 4-Coloring of unit segments, we show a
weaker ETH lower bound of which exploits the celebrated
Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over
to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent
Dominating Set.Comment: 19 pages, 15 figure
LIBOPT - An environment for testing solvers on heterogeneous collections of problems - Version 1.0
The Libopt environment is both a methodology and a set of tools that can be
used for testing, comparing, and profiling solvers on problems belonging to
various collections. These collections can be heterogeneous in the sense that
their problems can have common features that differ from one collection to the
other. Libopt brings a unified view on this composite world by offering, for
example, the possibility to run any solver on any problem compatible with it,
using the same Unix/Linux command. The environment also provides tools for
comparing the results obtained by solvers on a specified set of problems. Most
of the scripts going with the Libopt environment have been written in Perl
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