Design of multiunit electronic exchanges through decomposition

In this paper, we exploit the idea of decomposition to match buyers and sellers in an electronic exchange for trading large volumes of homogeneous goods, where the buyers and sellers specify marginal-decreasing piecewise constant price curves to capture volume discounts. Such exchanges are relevant for automated trading in many e-business applications. The problem of determining winners and Vickrey prices in such exchanges is known to have a worst-case complexity equal to that of as many as (1 + m + n) NP-hard problems, where m is the number of buyers and n is the number of sellers. Our method proposes the overall exchange problem to be solved as two separate and simpler problems: 1) forward auction and 2) reverse auction, which turns out to be generalized knapsack problems. In the proposed approach, we first determine the quantity of units to be traded between the sellers and the buyers using fast heuristics developed by us. Next, we solve a forward auction and a reverse auction using fully polynomial time approximation schemes available in the literature. The proposed approach has worst-case polynomial time complexity. and our experimentation shows that the approach produces good quality solutions to the problem. Note to Practitioners- In recent times, electronic marketplaces have provided an efficient way for businesses and consumers to trade goods and services. The use of innovative mechanisms and algorithms has made it possible to improve the efficiency of electronic marketplaces by enabling optimization of revenues for the marketplace and of utilities for the buyers and sellers. In this paper, we look at single-item, multiunit electronic exchanges. These are electronic marketplaces where buyers submit bids and sellers ask for multiple units of a single item. We allow buyers and sellers to specify volume discounts using suitable functions. Such exchanges are relevant for high-volume business-to-business trading of standard products, such as silicon wafers, very large-scale integrated chips, desktops, telecommunications equipment, commoditized goods, etc. The problem of determining winners and prices in such exchanges is known to involve solving many NP-hard problems. Our paper exploits the familiar idea of decomposition, uses certain algorithms from the literature, and develops two fast heuristics to solve the problem in a near optimal way in worst-case polynomial time.

Properties of the correlated electronic states of pyrene and hydrogenated pyrene

Approximate calculations are reported on pyrene within the PPP model Hamiltonian using a novel restricted CI scheme which employs both molecular orbital and valence bond techniques. Also reported are detailed full CI results of the PPP model on 2,7-dihydropyrene obtained using the valence bond method. Spectral studies, charge and spin density calculations in ground and excited states, and ring current calculations in the ground state of the molecules are presented. In pyrene, the calculated excitation energies are in good agreement with experiment. The closed structure pi-conjugated molecule pyrene appears to show smaller distortions from the ground state geometry compared with the open structure pi-conjugated molecule 2,7-dihydropyrene. The ground state equilibrium structure of 2,7-dihydropyrene can be viewed as two hexatriene molecules connected by a vinyl crosslink, as is evident from bond order and ring current calculations. This is consistent with the only Kekule resonant structure possible for this molecule.

Electronic Control of Facial Selection in Additions to Sterically Unbiased Ketones and Olefins

By definition, the two faces of a pi bond are equivalent.1 However, they are rendered nonequivalent in most molecules because of the absence of a plane of symmetry encompassing the double bond and the adjacent substituents. As a result, additions to trigonal centers from the two faces need not be equally facile. Exploiting this stereodifferentiation in a controlled manner represents one of the core problems in organic synthesis. Evidently, the factors which determine such diastereoselection need to be delineated in as much detail as possible.

Electronic Properties of the Vortex State in Cuprate Superconductors

The superconducting state of the cuprates in the presence of a magnetic field has been investigated very actively in the past few years through measurements of electrical and thermal transport, ac conductivity, specific heat, and other quantities. The observed behavior is not well understood; it probes the nature of quasiparticies, vortices, and their interactions in a superconductor with nodes in the pair amplitude. We summarize here experimental results and our attempts to understand the phenomena.