Polynomiality for Bin Packing with a Constant Number of Item Types

We consider the bin packing problem with d different item sizes s_i and item multiplicities a_i, where all numbers are given in binary encoding. This problem formulation is also known as the 1-dimensional cutting stock problem. In this work, we provide an algorithm which, for constant d, solves bin packing in polynomial time. This was an open problem for all d >= 3. In fact, for constant d our algorithm solves the following problem in polynomial time: given two d-dimensional polytopes P and Q, find the smallest number of integer points in P whose sum lies in Q. Our approach also applies to high multiplicity scheduling problems in which the number of copies of each job type is given in binary encoding and each type comes with certain parameters such as release dates, processing times and deadlines. We show that a variety of high multiplicity scheduling problems can be solved in polynomial time if the number of job types is constant

The Commercial Music Industry in Atlanta and the State of Georgia: An Economic Impact Study

This study was prepared to ascertain the magnitude of the commercial music industry's economic impact on Atlanta and its surrounding areas. Report #8

Comments on lattice gauge theories with infrared-attractive fixed points

Theories of interacting gauge fields and fermions can possess a running gauge coupling with an infrared attractive fixed point (IRFP). We present a minimal description of the physics of these systems and comment on some simple expectations for results from lattice simulations done within the basin of attraction of the IRFP in these theories.Comment: 10 pages, 2 figures. Published version, fixed typos in version

Combinatorial analysis of interacting RNA molecules

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.Comment: 22 pages, 15 figure

Studying Intermediate pT Hadron Production with Fluctuations

Mechanisms for particle production at intermediate pT in nuclear collisions at RHIC are discussed, emphasizing the differences in associated jet-like correlations between color-neutral and colored production. An alternative production mechanism involving both recombination and fragmentation is suggested, which might simultaneously lead to an enhancement of baryons and to jet-like correlations. To gain more insight into the relative importance of different mechanisms a study of constrained distributions of associated multiplicity is proposed. In a simple model it is shown that these multiplicity distributions may change significantly, if the nature of the production mechanism fluctuates from event to event.Comment: 7 pages, 4 figures, talk at Hot Quarks 2004 conferenc

QCD Factorization in BB Decays into ρπ\rho \pi

Based on the QCD factorization approach we analyse the branching ratios for the channel $B \to \rho \pi$. From the comparisons with experimental data provided by CLEO, BELLE and BABAR we constrain the form factor $F^{B \to \pi}(m_{\rho}^{2})$ and propose boundaries for this form factor depending on the CKM matrix element parameters $\rho$ and $\eta$.Comment: 11 pages, 9 figures. Talk presented at Fourth Tropical Workshop, Cairns, Australia, 9--13 June 2003. Proceedings to be published by AI