Contractions, Removals and How to Certify 3-Connectivity in Linear Time

It is well-known as an existence result that every 3-connected graph G=(V,E) on more than 4 vertices admits a sequence of contractions and a sequence of removal operations to K_4 such that every intermediate graph is 3-connected. We show that both sequences can be computed in optimal time, improving the previously best known running times of O(|V|^2) to O(|V|+|E|). This settles also the open question of finding a linear time 3-connectivity test that is certifying and extends to a certifying 3-edge-connectivity test in the same time. The certificates used are easy to verify in time O(|E|).Comment: preliminary versio

Edge-Orders

Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a graph decomposition into parts that have a prescribed vertex-connectivity. Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-edge-connected graphs in linear time, respectively. While the former can be seen as the edge-variants of st-numberings, the latter are the edge-variants of Mondshein sequences and non-separating ear decompositions. The methods that we use for obtaining such edge-orders differ considerably in almost all details from the ones used for their vertex-counterparts, as different graph-theoretic constructions are used in the inductive proof and standard reductions from edge- to vertex-connectivity are bound to fail. As a first application, we consider the famous Edge-Independent Spanning Tree Conjecture, which asserts that every k-edge-connected graph contains k rooted spanning trees that are pairwise edge-independent. We illustrate the impact of the above edge-orders by deducing algorithms that construct 2- and 3-edge independent spanning trees of 2- and 3-edge-connected graphs, the latter of which improves the best known running time from O(n^2) to linear time

Dispersive regime of the Jaynes-Cummings and Rabi lattice

Photon-based strongly-correlated lattice models like the Jaynes-Cummings and Rabi lattices differ from their more conventional relatives like the Bose-Hubbard model by the presence of an additional tunable parameter: the frequency detuning between the pseudo-spin degree of freedom and the harmonic mode frequency on each site. Whenever this detuning is large compared to relevant coupling strengths, the system is said to be in the dispersive regime. The physics of this regime is well-understood at the level of a single Jaynes-Cummings or Rabi site. Here, we extend the theoretical description of the dispersive regime to lattices with many sites, for both strong and ultra-strong coupling. We discuss the nature and spatial range of the resulting qubit-qubit and photon-photon coupling, demonstrate the emergence of photon- pairing and squeezing, and illustrate our results by exact diagonalization of the Rabi dimer.Comment: 22 pages, 7 figures, 1 table, Published by NJP, Focus Issues "Focus on Quantum Microwave Field Effects in Superconducting Circuits

Research Efficiency in Manufacturing: An Application of DEA at the Industry Level

This paper analyzes research efficiency at the industry level in manufacturing for 13 European member and four nonmember countries during 2000 and 2004. A unique dataset was compiled that matches patent applications at the European Patent Office (EPO) to industry-specific R&D inputs from EU KLEMS. We find that Germany, the United States, and Denmark have the highest efficiency scores on average in total manufacturing. The main industries that are at the technology frontier are those involved in electrical and optical equipment and machinery. Separate frontier estimations for these industries, conducted without the constraint of a constant technology frontier, provide additional support for our results.R&D efficiency, industry level, data envelopment analysis, manufacturing

Empiricism Meets Theory: Is the Boone-Indicator Applicable?

Boone (2008a) proposes a new competition measure based on Relative Profit Differences (RPD) with superior theoretical properties. However, the empirical applicability and robust-ness of the Boone-Indicator is still unknown. This paper aims to address that question. Using a rich, newly built, data set for German manufacturing enterprises, we test the empirical valid-ity of the Boone-Indicator using cartel cases. Our analysis reveals that the traditional regres-sion approach of the indicator fails to correctly indicate competition. A proposed augmented indicator based on RPDs performs better. The traditional Lerner-Index is still the only meas-ure that correctly indicates the expected competitive changes.Competition, Boone-Indicator, Cartels, Census Data

Technology Portfolio and Market Value

This paper discusses the impact of a firm's technology portfolio on its market value. Two concepts are used to characterize a firm's portfolio: the number of technological fields and the degree of relatedness within the portfolio characterized by the amount of joint occurrences of patents in technological fields. Based on a theoretical framework using an expanded Tobin's q approach, it presents evidence for a negative influence of portfolio size on the market value caused by a diminishing potential to make use of economies of scale. This discount can be counterbalanced when the relevant fields share a common technological base which is measured by the degree of technological relatedness.technological portfolio, relatedness, patent statistics, tobin's q, economies of scope