528 research outputs found
Thresholded Covering Algorithms for Robust and Max-Min Optimization
The general problem of robust optimization is this: one of several possible
scenarios will appear tomorrow, but things are more expensive tomorrow than
they are today. What should you anticipatorily buy today, so that the
worst-case cost (summed over both days) is minimized? Feige et al. and
Khandekar et al. considered the k-robust model where the possible outcomes
tomorrow are given by all demand-subsets of size k, and gave algorithms for the
set cover problem, and the Steiner tree and facility location problems in this
model, respectively.
In this paper, we give the following simple and intuitive template for
k-robust problems: "having built some anticipatory solution, if there exists a
single demand whose augmentation cost is larger than some threshold, augment
the anticipatory solution to cover this demand as well, and repeat". In this
paper we show that this template gives us improved approximation algorithms for
k-robust Steiner tree and set cover, and the first approximation algorithms for
k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios
(except for multicut) are almost best possible.
As a by-product of our techniques, we also get algorithms for max-min
problems of the form: "given a covering problem instance, which k of the
elements are costliest to cover?".Comment: 24 page
Snail Homing and Mating Search Algorithm: A Novel Bio-Inspired Metaheuristic Algorithm
In this paper, a novel Snail Homing and Mating Search (SHMS) algorithm is
proposed. It is inspired from the biological behaviour of the snails. Snails
continuously travels to find food and a mate, leaving behind a trail of mucus
that serves as a guide for their return. Snails tend to navigate by following
the available trails on the ground and responding to cues from nearby shelter
homes. The proposed SHMS algorithm is investigated by solving several unimodal
and multimodal functions. The solutions are validated using standard
statistical tests such as two-sided and pairwise signed rank Wilcoxon test and
Friedman rank test. The solution obtained from the SHMS algorithm exhibited
superior robustness as well as search space exploration capabilities within the
less computational cost. The real-world application of SHMS algorithm is
successfully demonstrated in the engineering design domain by solving three
cases of design and economic optimization shell and tube heat exchanger
problem. The objective function value and other statistical results obtained
using SHMS algorithm are compared with other well-known metaheuristic
algorithms.Comment: 46 Pages, 11 Figures, 24 Table
Energy saving in fixed wireless broadband networks
International audienceIn this paper, we present a mathematical formulation for saving energy in fixed broadband wireless networks by selectively turning off idle communication devices in low-demand scenarios. This problem relies on a fixed-charge capacitated network design (FCCND), which is very hard to optimize. We then propose heuristic algorithms to produce feasible solutions in a short time.Dans cet article, nous proposons une modélisation en programme linéaire en nombres entiers pour le problème de minimiser la consommation d'énergie dans les réseaux de collecte à faisceaux hertziens en éteignant une partie des équipements lorsque le trafic est bas. Ce problème repose sur un problème de dimensionnement de réseaux dont les arcs ont une capacité fixe, qui est très difficile à résoudre. Nous proposons un algorithme heuristique fournissant rapidement des solutions réalisables
Noncommutativity in a Time-Dependent Background
We compute a time-dependent noncommutativity parameter in a model with a
time-dependent background, a space-time metric of the plane wave type supported
by a Neveu-Schwarz two-form potential. This model is an open string version of
the WZW model based on a non-semi-simple group previously studied by Nappi and
Witten. The background we study is not conformally invariant. We consider a
light-cone action for the sigma-model, compute the worldsheet propagator, and
use it to derive a time-dependent noncommutativity parameter.Comment: 12 pages; v3: statement corrected and references adde
Brownian Motion and Polymer Statistics on Certain Curved Manifolds
We have calculated the probability distribution function G(R,L|R',0) of the
end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a
Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a
cylinder, a cone and a curved torus in 3-D.
We showed that: surface curvature induces a geometrical localization area; at
short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at
large scales, (R-R')^2 is constant for the sphere, it is linear in L for the
cylinder and reaches different constant values for the torus. The cone vertex
induces (function of opening angle and R') contraction of the chain for all
lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to
appear in Phys. Rev
Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator
In the Heisenberg picture, the generalized invariant and exact quantum
motions are found for a time-dependent forced harmonic oscillator. We find the
eigenstate and the coherent state of the invariant and show that the
dispersions of these quantum states do not depend on the external force. Our
formalism is applied to several interesting cases.Comment: 15 pages, two eps files, to appear in Phys. Rev. A 53 (6) (1996
Field theoretic description of charge regulation interaction
In order to find the exact form of the electrostatic interaction between two
proteins with dissociable charge groups in aqueous solution, we have studied a
model system composed of two macroscopic surfaces with charge dissociation
sites immersed in a counterion-only ionic solution. Field-theoretic
representation of the grand canonical partition function is derived and
evaluated within the mean-field approximation, giving the Poisson-Boltzmann
theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations
around the mean-field are then analyzed in the lowest order correction that we
calculate analytically and exactly, using the path integral representation for
the partition function of a harmonic oscillator with time-dependent frequency.
The first order (one loop) free energy correction gives the interaction free
energy that reduces to the zero-frequency van der Waals form in the appropriate
limit but in general gives rise to a mono-polar fluctuation term due to charge
fluctuation at the dissociation sites. Our formulation opens up the possibility
to investigate the Kirkwood-Shumaker interaction in more general contexts where
their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ
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