95,794 research outputs found
An approach for generating different types of gray codes
Given a certain Gray code consisting of 2n codewords, it is possible to generate from it n! 2n codes by permuting and/or complementing the bits in all the codewords in the same manner. The codes obtained this way are all defined to be of the same type. An approach for converting the standard Gray code (known as the reflected code) into other Gray codes of different types is presented in this paper. A systematic way of generating, for example, all types of Gray codes consisting of 16 codewords is given
Combinatorial generation via permutation languages
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations.
This approach provides a unified view on many known results and allows us to prove many new ones.
In particular, we obtain the following four classical Gray codes as special cases: the Steinhaus-Johnson-Trotter algorithm to generate all permutations of an -element set by adjacent transpositions; the binary reflected Gray code to generate all -bit strings by flipping a single bit in each step; the Gray code for generating all -vertex binary trees by rotations due to Lucas, van Baronaigien, and Ruskey; the Gray code for generating all partitions of an -element ground set by element exchanges due to Kaye.
We present two distinct applications for our new framework:
The first main application is the generation of pattern-avoiding permutations, yielding new Gray codes for different families of permutations that are characterized by the avoidance of certain classical patterns, (bi)vincular patterns, barred patterns, Bruhat-restricted patterns, mesh patterns, monotone and geometric grid classes, and many others.
We thus also obtain new Gray code algorithms for the combinatorial objects that are in bijection to these permutations, in particular for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into rectangles subject to certain restrictions.
The second main application of our framework are lattice congruences of the weak order on the symmetric group~.
Recently, Pilaud and Santos realized all those lattice congruences as -dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc.
Our algorithm generates the equivalence classes of each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian.
We thus also obtain a provable notion of optimality for the Gray codes obtained from our framework: They translate into walks along the edges of a polytope
Combinatorial generation via permutation languages. I. Fundamentals
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations.
This approach provides a unified view on many known results and allows us to prove many new ones.
In particular, we obtain the following four classical Gray codes as special cases: the Steinhaus-Johnson-Trotter algorithm to generate all permutations of an -element set by adjacent transpositions; the binary reflected Gray code to generate all -bit strings by flipping a single bit in each step; the Gray code for generating all -vertex binary trees by rotations due to Lucas, van Baronaigien, and Ruskey; the Gray code for generating all partitions of an -element ground set by element exchanges due to Kaye.
We present two distinct applications for our new framework:
The first main application is the generation of pattern-avoiding permutations, yielding new Gray codes for different families of permutations that are characterized by the avoidance of certain classical patterns, (bi)vincular patterns, barred patterns, boxed patterns, Bruhat-restricted patterns, mesh patterns, monotone and geometric grid classes, and many others.
We also obtain new Gray codes for all the combinatorial objects that are in bijection to these permutations, in particular for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into rectangles subject to certain restrictions.
The second main application of our framework are lattice congruences of the weak order on the symmetric group~.
Recently, Pilaud and Santos realized all those lattice congruences as -dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc.
Our algorithm generates the equivalence classes of each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian.
We thus also obtain a provable notion of optimality for the Gray codes obtained from our framework: They translate into walks along the edges of a polytope
DAugNet: Unsupervised, Multi-source, Multi-target, and Life-long Domain Adaptation for Semantic Segmentation of Satellite Images
The domain adaptation of satellite images has recently gained an increasing
attention to overcome the limited generalization abilities of machine learning
models when segmenting large-scale satellite images. Most of the existing
approaches seek for adapting the model from one domain to another. However,
such single-source and single-target setting prevents the methods from being
scalable solutions, since nowadays multiple source and target domains having
different data distributions are usually available. Besides, the continuous
proliferation of satellite images necessitates the classifiers to adapt to
continuously increasing data. We propose a novel approach, coined DAugNet, for
unsupervised, multi-source, multi-target, and life-long domain adaptation of
satellite images. It consists of a classifier and a data augmentor. The data
augmentor, which is a shallow network, is able to perform style transfer
between multiple satellite images in an unsupervised manner, even when new data
are added over the time. In each training iteration, it provides the classifier
with diversified data, which makes the classifier robust to large data
distribution difference between the domains. Our extensive experiments prove
that DAugNet significantly better generalizes to new geographic locations than
the existing approaches
- …