On the Asymptotic Worst Case Behavior of Harmonic Fit

In the parametric bin packing problem we must pack a list of items with size smaller than or equal to 1/r in a minimal number of unit-capacity bins. Among the approximation algorithms, the class of Harmonic Fit algorithms (HFM) plays an important role. Lee and Lee (J. Assoc. Comput. Mach. 32 (1985), 562-572) and Galambos (Ann. Univ. Sci. Budapest Sect. Comput. 9 (1988), 121-126) provide upper bounds for the asymptotic worst case ratio of HFM and show tightness for certain values of the parameter M. In this paper we provide worst case examples that meet the known upper bound for additional values of M, and we show that for remaining values of M the known upper bound is not tight. For the classical bin packing problem (r = 1), we prove an asymptotic worst case ratio of 12/7 for the case M = 4 and 1.7 for the case M = 5. We give improved lower bounds for some interesting cases that are left open

On-line bin-packing problem : maximizing the number of unused bins

In this paper, we study the on-line version of the bin-packing problem. We analyze the approximation behavior of an on-line bin-packing algorithm under an approximation criterion called differential ratio. We are interested in two types of results : the differential competitivity ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problem and for the quality of the algorithm developed to solve it. In its off-line version, the bin-packing problem, BP, is better approximated in differential framework than in standard one. Our objective is to determine if or not such result exists for the on-line version of BP.On-line algorithm, bin-packing problem, competitivity ratio.

Probabilistic alternatives for competitive analysis

In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: it sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.operations research and management science;

Critical Analysis of Theoretical Estimates for BB to Light Meson Form Factors and the B→ψK(K∗)B \to \psi K(K^{\ast}) Data

We point out that current estimates of form factors fail to explain the non-leptonic decays $B \to \psi K(K^{\ast})$ and that the combination of data on the semi-leptonic decays $D \to K(K^{\ast})\ell \nu$ and on the non-leptonic decays $B \to \psi K(K^{\ast})$ (in particular recent po\-la\-ri\-za\-tion data) severely constrain the form (normalization and $q^2$ dependence) of the heavy-to-light meson form factors, if we assume the factorization hypothesis for the latter. From a simultaneous fit to \bpsi and \dk data we find that strict heavy quark limit scaling laws do not hold when going from $D$ to $B$ and must have large corrections that make softer the dependence on the masses. We find that $A_1(q^2)$ should increase slower with \qq than $A_2, V, f_+$. We propose a simple parametrization of these corrections based on a quark model or on an extension of the \hhs laws to the \hl case, complemented with an approximately constant $A_1(q^2)$. We analyze in the light of these data and theoretical input various theoretical approaches (lattice calculations, QCD sum rules, quark models) and point out the origin of the difficulties encountered by most of these schemes. In particular we check the compatibility of several quark models with the heavy quark scaling relations.Comment: 48 pages, DAPNIA/SPP/94-24, LPTHE-Orsay 94/1

Supernova pointing with low- and high-energy neutrino detectors

A future galactic SN can be located several hours before the optical explosion through the MeV-neutrino burst, exploiting the directionality of $\nu$-$e$-scattering in a water Cherenkov detector such as Super-Kamiokande. We study the statistical efficiency of different methods for extracting the SN direction and identify a simple approach that is nearly optimal, yet independent of the exact SN neutrino spectra. We use this method to quantify the increase in the pointing accuracy by the addition of gadolinium to water, which tags neutrons from the inverse beta decay background. We also study the dependence of the pointing accuracy on neutrino mixing scenarios and initial spectra. We find that in the ``worst case'' scenario the pointing accuracy is $8^\circ$ at 95% C.L. in the absence of tagging, which improves to $3^\circ$ with a tagging efficiency of 95%. At a megaton detector, this accuracy can be as good as $0.6^\circ$. A TeV-neutrino burst is also expected to be emitted contemporaneously with the SN optical explosion, which may locate the SN to within a few tenths of a degree at a future km$^2$ high-energy neutrino telescope. If the SN is not seen in the electromagnetic spectrum, locating it in the sky through neutrinos is crucial for identifying the Earth matter effects on SN neutrino oscillations.Comment: 13 pages, 7 figures, Revtex4 format. The final version to be published in Phys. Rev. D. A few points in the original text are clarifie

Small-World Rouse Networks as models of cross-linked polymers

We use the recently introduced small-world networks (SWN) to model cross-linked polymers, as an extension of the linear Rouse-chain. We study the SWN-dynamics under the influence of external forces. Our focus is on the structurally and thermally averaged SWN stretching, which we determine both numerically and analytically using a psudo-gap ansatz for the SWN-density of states. The SWN stretching is related to the probability of a random-walker to return to its origin on the SWN. We compare our results to the corresponding ones for Cayley trees.Comment: 14 pages, 4 figures. Preprint version, submitted to JC