88 research outputs found
On vertex adjacencies in the polytope of pyramidal tours with step-backs
We consider the traveling salesperson problem in a directed graph. The
pyramidal tours with step-backs are a special class of Hamiltonian cycles for
which the traveling salesperson problem is solved by dynamic programming in
polynomial time. The polytope of pyramidal tours with step-backs is
defined as the convex hull of the characteristic vectors of all possible
pyramidal tours with step-backs in a complete directed graph. The skeleton of
is the graph whose vertex set is the vertex set of and the
edge set is the set of geometric edges or one-dimensional faces of .
The main result of the paper is a necessary and sufficient condition for vertex
adjacencies in the skeleton of the polytope that can be verified in
polynomial time.Comment: in Englis
A reconstruction of the initial conditions of the Universe by optimal mass transportation
Reconstructing the density fluctuations in the early Universe that evolved
into the distribution of galaxies we see today is a challenge of modern
cosmology [ref.]. An accurate reconstruction would allow us to test
cosmological models by simulating the evolution starting from the reconstructed
state and comparing it to the observations. Several reconstruction techniques
have been proposed [8 refs.], but they all suffer from lack of uniqueness
because the velocities of galaxies are usually not known. Here we show that
reconstruction can be reduced to a well-determined problem of optimisation, and
present a specific algorithm that provides excellent agreement when tested
against data from N-body simulations. By applying our algorithm to the new
redshift surveys now under way [ref.], we will be able to recover reliably the
properties of the primeval fluctuation field of the local Universe and to
determine accurately the peculiar velocities (deviations from the Hubble
expansion) and the true positions of many more galaxies than is feasible by any
other method.
A version of the paper with higher-quality figures is available at
http://www.obs-nice.fr/etc7/nature.pdfComment: Latex, 4 pages, 3 figure
An Adaptive Search for the Response Time Variability Problem
The Response Time Variability Problem (RTVP) is an NP-hard combinatorial scheduling problem,
which has recently been reported and formalised in the literature. This problem has a wide range of
real-world applications in mixed-model assembly lines, multi-threaded computer systems, broadcast of
commercial videotapes and others. The RTVP arises whenever products, clients or jobs need to be
sequenced in such a way that the variability in the time between the points at which they receive the
necessary resources is minimised. We propose a greedy but adaptive heuristic that avoids being trapped
into a poor solution by incorporating a look ahead strategy suitable for this particular scheduling
problem. The proposed heuristic outperforms the best existing methods, while being much faster and
easier to understand and to implement
Goodness-of-fit Criteria for the Adams and Jefferson Rounding Methods and their Limiting Laws
Apportionment method, q-Stationary multiplier method, Rounding error analysis, Sainte–Laguë divergence, Convergence in distribution, Gaussian limit law,
- …