285 research outputs found
Algebraic symmetries of generic dimensional periodic Costas arrays
In this work we present two generators for the group of symmetries of the
generic dimensional periodic Costas arrays over elementary abelian
groups: one that is defined by multiplication on
dimensions and the other by shear (addition) on dimensions. Through
exhaustive search we observe that these two generators characterize the group
of symmetries for the examples we were able to compute. Following the results,
we conjecture that these generators characterize the group of symmetries of the
generic dimensional periodic Costas arrays over elementary abelian
groups
Use of Costas arrays in subpixel metrology
Subpixel methods increase the accuracy and efficiency of image detectors, processing units, and algorithms and provide very cost-effective systems for object tracking. A recently proposed method permits micropixel and submicropixel accuracies providing certain design constraints on the target are met. In this paper, we explore the use of Costas arrays - permutation matrices with ideal auto-ambiguity properties - for the design of such targets.JJH acknowledges the support of the National University of Ireland (NUI) Post-doctoral Fellowship in the Sciences. DM acknowledges the support of the Spanish Ministerio de EconomÃa y Competitividad through the project BIA2011-22704, the Generalitat Valenciana through the project PROMETEO/2011/021, and the University of Alicante through the project GRE10-09. The authors also would like to acknowledge the support of Science Foundation Ireland and Enterprise Ireland under the National Development Plan
Honeycomb Arrays
A honeycomb array is an analogue of a Costas array in the hexagonal grid; they
were first studied by Golomb and Taylor in 1984. A recent result of Blackburn,
Etzion, Martin and Paterson has shown that (in contrast to the situation for Costas
arrays) there are only finitely many examples of honeycomb arrays, though their
bound on the maximal size of a honeycomb array is too large to permit an exhaustive
search over all possibilities.
The present paper contains a theorem that significantly limits the number of possibilities
for a honeycomb array (in particular, the theorem implies that the number
of dots in a honeycomb array must be odd). Computer searches for honeycomb
arrays are summarised, and two new examples of honeycomb arrays with 15 dots
are given
Large-scale parallelism for constraint-based local search: the costas array case study
International audienceWe present the parallel implementation of a constraint-based Local Search algorithm and investigate its performance on several hardware plat-forms with several hundreds or thousands of cores. We chose as the basis for these experiments the Adaptive Search method, an efficient sequential Local Search method for Constraint Satisfaction Problems (CSP). After preliminary experiments on some CSPLib benchmarks, we detail the modeling and solving of a hard combinatorial problem related to radar and sonar applications: the Costas Array Problem. Performance evaluation on some classical CSP bench-marks shows that speedups are very good for a few tens of cores, and good up to a few hundreds of cores. However for a hard combinatorial search problem such as the Costas Array Problem, performance evaluation of the sequential version shows results outperforming previous Local Search implementations, while the parallel version shows nearly linear speedups up to 8,192 cores. The proposed parallel scheme is simple and based on independent multi-walks with no communication between processes during search. We also investigated a cooperative multi-walk scheme where processes share simple information, but this scheme does not seem to improve performance
Monomer-dimer tatami tilings of square regions
We prove that the number of monomer-dimer tilings of an square
grid, with monomers in which no four tiles meet at any point is
, when and have the same parity. In addition, we
present a new proof of the result that there are such tilings with
monomers, which divides the tilings into classes of size . The
sum of these tilings over all monomer counts has the closed form
and, curiously, this is equal to the sum of the squares of
all parts in all compositions of . We also describe two algorithms and a
Gray code ordering for generating the tilings with monomers,
which are both based on our new proof.Comment: Expanded conference proceedings: A. Erickson, M. Schurch, Enumerating
tatami mat arrangements of square grids, in: 22nd International Workshop on
Combinatorial Al- gorithms (IWOCA), volume 7056 of Lecture Notes in Computer
Science (LNCS), Springer Berlin / Heidelberg, 2011, p. 12 pages. More on
Tatami tilings at
http://alejandroerickson.com/joomla/tatami-blog/collected-resource
A Computational Comparison of Optimization Methods for the Golomb Ruler Problem
The Golomb ruler problem is defined as follows: Given a positive integer n,
locate n marks on a ruler such that the distance between any two distinct pair
of marks are different from each other and the total length of the ruler is
minimized. The Golomb ruler problem has applications in information theory,
astronomy and communications, and it can be seen as a challenge for
combinatorial optimization algorithms. Although constructing high quality
rulers is well-studied, proving optimality is a far more challenging task. In
this paper, we provide a computational comparison of different optimization
paradigms, each using a different model (linear integer, constraint programming
and quadratic integer) to certify that a given Golomb ruler is optimal. We
propose several enhancements to improve the computational performance of each
method by exploring bound tightening, valid inequalities, cutting planes and
branching strategies. We conclude that a certain quadratic integer programming
model solved through a Benders decomposition and strengthened by two types of
valid inequalities performs the best in terms of solution time for small-sized
Golomb ruler problem instances. On the other hand, a constraint programming
model improved by range reduction and a particular branching strategy could
have more potential to solve larger size instances due to its promising
parallelization features
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