1,146 research outputs found
Low-Degree Spanning Trees of Small Weight
The degree-d spanning tree problem asks for a minimum-weight spanning tree in
which the degree of each vertex is at most d. When d=2 the problem is TSP, and
in this case, the well-known Christofides algorithm provides a
1.5-approximation algorithm (assuming the edge weights satisfy the triangle
inequality).
In 1984, Christos Papadimitriou and Umesh Vazirani posed the challenge of
finding an algorithm with performance guarantee less than 2 for Euclidean
graphs (points in R^n) and d > 2. This paper gives the first answer to that
challenge, presenting an algorithm to compute a degree-3 spanning tree of cost
at most 5/3 times the MST. For points in the plane, the ratio improves to 3/2
and the algorithm can also find a degree-4 spanning tree of cost at most 5/4
times the MST.Comment: conference version in Symposium on Theory of Computing (1994
Optimisation of quantum Monte Carlo wave function: steepest descent method
We have employed the steepest descent method to optimise the variational
ground state quantum Monte Carlo wave function for He, Li, Be, B and C atoms.
We have used both the direct energy minimisation and the variance minimisation
approaches. Our calculations show that in spite of receiving insufficient
attention, the steepest descent method can successfully minimise the wave
function. All the derivatives of the trial wave function respect to spatial
coordinates and variational parameters have been computed analytically. Our
ground state energies are in a very good agreement with those obtained with
diffusion quantum Monte Carlo method (DMC) and the exact results.Comment: 13 pages, 3 eps figure
Approximating the Minimum Equivalent Digraph
The MEG (minimum equivalent graph) problem is, given a directed graph, to
find a small subset of the edges that maintains all reachability relations
between nodes. The problem is NP-hard. This paper gives an approximation
algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its
analysis are based on the simple idea of contracting long cycles. (This result
is strengthened slightly in ``On strongly connected digraphs with bounded cycle
length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local
improvement'' algorithm, showing that its performance guarantee is 1.75.Comment: conference version in ACM-SIAM Symposium on Discrete Algorithms
(1994
Magnetic Properties of Undoped
The Heisenberg antiferromagnet, which arises from the large Hubbard
model, is investigated on the molecule and other fullerenes. The
connectivity of leads to an exotic classical ground state with
nontrivial topology. We argue that there is no phase transition in the Hubbard
model as a function of , and thus the large solution is relevant for
the physical case of intermediate coupling. The system undergoes a first order
metamagnetic phase transition. We also consider the S=1/2 case using
perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included
Synchronization time in a hyperbolic dynamical system with long-range interactions
We show that the threshold of complete synchronization in a lattice of
coupled non-smooth chaotic maps is determined by linear stability along the
directions transversal to the synchronization subspace. We examine carefully
the sychronization time and show that a inadequate observation of the system
evolution leads to wrong results. We present both careful numerical experiments
and a rigorous mathematical explanation confirming this fact, allowing for a
generalization involving hyperbolic coupled map lattices.Comment: 22 pages (preprint format), 4 figures - accepted for publication in
Physica A (June 28, 2010
Effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems
We study the effect of randomness and anisotropy on Turing patterns in
reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of
pattern formation is considered. The cases we study are: (i)randomness in the
underlying lattice structure, (ii)the case in which there is a probablity p
that at a lattice site both reaction and diffusion occur, otherwise there is
only diffusion and lastly, the effect of (iii) anisotropic and (iv) random
diffusion coefficients on the formation of Turing patterns. The general
conclusion is that the Turing mechanism of pattern formation is fairly robust
in the presence of randomness and anisotropy.Comment: 11 pages LaTeX, 14 postscript figures, accepted in Phys. Rev.
Balancing Minimum Spanning and Shortest Path Trees
This paper give a simple linear-time algorithm that, given a weighted
digraph, finds a spanning tree that simultaneously approximates a shortest-path
tree and a minimum spanning tree. The algorithm provides a continuous
trade-off: given the two trees and epsilon > 0, the algorithm returns a
spanning tree in which the distance between any vertex and the root of the
shortest-path tree is at most 1+epsilon times the shortest-path distance, and
yet the total weight of the tree is at most 1+2/epsilon times the weight of a
minimum spanning tree. This is the best tradeoff possible. The paper also
describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993
Electron correlation in C_(4N+2) carbon rings: aromatic vs. dimerized structures
The electronic structure of C_(4N+2) carbon rings exhibits competing
many-body effects of Huckel aromaticity, second-order Jahn-Teller and Peierls
instability at large sizes. This leads to possible ground state structures with
aromatic, bond angle or bond length alternated geometry. Highly accurate
quantum Monte Carlo results indicate the existence of a crossover between C_10
and C_14 from bond angle to bond length alternation. The aromatic isomer is
always a transition state. The driving mechanism is the second-order
Jahn-Teller effect which keeps the gap open at all sizes.Comment: Submitted for publication: 4 pages, 3 figures. Corrected figure
Vibrational signatures for low-energy intermediate-sized Si clusters
We report low-energy locally stable structures for the clusters Si20 and Si21. The structures were obtained by performing geometry optimizations within the local density approximation. Our calculated binding energies for these clusters are larger than any previously reported for this size regime. To aid in the experimental identification of the structures, we have computed the full vibrational spectra of the clusters, along with the Raman and IR activities of the various modes using a recently developed first-principles technique. These represent, to our knowledge, the first calculations of Raman and IR spectra for Si clusters of this size
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