What to expect when trading with the U.S.S.R.: The Problems Confronting The American Exporter

An examination of the ramifications of the 1972 Trade Agreement between the United States and the Soviet Union

Antitrust Enforcement Encourages Health Care Providers to Cooperate Procompetitively

A review of significant administrative and judicial rulings in antitrust law during 1993 shows that the antitrust laws should not impede innovative, cost-cutting cooperative arrangements among providers, so long as their actual or potential procompetitive benefits are not outweighed by their anticompetitive effects

Characteristics of Injuries in the Logging Industry of Louisiana, USA: 1986 to 1998

Characterizing injuries and their trends will allow safety managers to concentrate their resources on the areas of safety that will be most effective in the workplace. Injuries reported to the Louisiana Office of Workers' Compensation Administration for 1986 to 1998 were characterized according to the part of the body affected, the nature of the injury, the source of the injury, and the type of accident for the timber harvesting industry. Many of the injuries in the logging sector were sprains / strains to the knees. Injuries resulting from falling onto structures and surfaces were common and rising. Although the number of accidents in each category is generally decreasing, some trends should be of concern. There was no significant linear trend in overall accident rates since 1991. While the proportion of cuts and lacerations declined, the proportion of fractures increased. This coincided with a time period when logging operations in Louisiana experienced rapid mechanization and insurance companies started enforcing the use of personal protective equipment. The proportion of transportation accidents rose more than any other category. Some suggestions on focusing and improving current safety programs are given. The need for continued and improved training of managers and employees seems to be most critical

Polynomial Kernels for Weighted Problems

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for Subset Sum and Knapsack when parameterized by the number $n$ of items. We answer both questions affirmatively by using an algorithm for compressing numbers due to Frank and Tardos (Combinatorica 1987). This result had been first used by Marx and V\'egh (ICALP 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for Subset Sum and an exponential kernelization for Knapsack. Finally, we also obtain kernelization results for polynomial integer programs

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page