Coalition structure generation over graphs

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members — that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph

Bioreactor Landfill Research and Demonstration Project Northern Oaks Landfill, Harrison, MI

A bioreactor landfill cell with 1.2-acre footprint was constructed, filled, operated, and monitored at Northern Oaks Recycling and Disposal Facility (NORDF) at Harrison, MI. With a filled volume of 74,239 cubic yards, the cell contained approximately 35,317 tons of municipal solid waste (MSW) and 20,777 tons of cover soil. It was laid on the slope of an existing cell but separated by a geosynthetic membrane liner. After the cell reached a design height of 60 feet, it was covered with a geosynthetic membrane cap. A three-dimensional monitoring system to collect data at 48 different locations was designed and installed during the construction phase of the bioreactor cell. Each location had a cluster of monitoring devices consisting of a probe to monitor moisture and temperature, a leachate collection basin, and a gas sampling port. An increase in moisture content of the MSW in the bioreactor cell was achieved by pumping leachate collected on-site from various other cells, as well as recirculation of leachate from the bioreactor landfill cell itself. Three types of leachate injection systems were evaluated in this bioreactor cell for their efficacy to distribute pumped leachate uniformly: a leachate injection pipe buried in a 6-ft wide horizontal stone mound, a 15-ft wide geocomposite drainage layer, and a 60-ft wide geocomposite drainage layer. All leachate injection systems were installed on top of the compacted waste surface. The distribution of water and resulting MSW moisture content throughout the bioreactor cell was found to be similar for the three designs. Water coming into and leaving the cell (leachate pumped in, precipitation, snow, evaporation, and collected leachate) was monitored in order to carry out a water balance. Using a leachate injection rate of 26 – 30 gal/yard3, the average moisture content increased from 25% to 35% (wet based) over the period of this study. One of the key aspects of this bioreactor landfill study was to evaluate bioreactor start up and performance in locations with colder climate. For lifts filled during the summer months, methane generation started within three months after completion of the lift. For lifts filled in winter months, very little methane production occurred even eight months after filling. The temperature data indicated that subzero or slightly above zero (oC) temperatures persisted for unusually long periods (more than six months) in the lifts filled during winter months. This was likely due to the high thermal insulation capability of the MSW and the low level of biological activity during start up. This observation indicates that bioreactor landfills located in cold climate and filled during winter months may require mechanisms to increase temperature and initiate biodegradation. Thus, besides moisture, temperature may be the next important factor controlling the biological decomposition in anaerobic bioreactor landfills. Spatial and temporal characterization of leachate samples indicated the presence of low levels of commonly used volatile organic compounds (including acetone, methyl ethyl ketone, methyl isobutyl ketone, and toluene) and metals (including arsenic, chromium, and zinc). Changes and leachate and gaseous sample characteristics correlated with enhanced biological activity and increase in temperature. Continued monitoring of this bioreactor landfill cell is expected to yield critical data needed for start up, design, and operation of this emerging process

Determination of partition coefficients and aqueous solubilities by reverse phase chromatography--II : Evaluation of partitioning and solubility models

Part I of this series examined the chemical and thermodynamic principles underlying the solubility and partitioning characteristics of non-electrolyte organic compounds in aqueous systems. It further considered those concepts which interrelate solubility and partitioning phenomena with retentive behavior in reverse phase liquid chromatography. Conceptual and predictive models which intercorrelate solubility, octanol/water partitioning, and reverse phase retention times were developed. Part II of the series evaluates the relative predictive abilities of these models for a wide range of different classes of organic pollutants. The results reveal that the reverse phase liquid chromatography models developed in Part I provide good estimates of octanol/water coefficients and aqueous solubilities from experimentally determined chromatographic retention times. Models structured to predict aqueous solubilities from octanol/water partition coefficient data were also found to provide reasonable estimates, but require as input physical and chemical parameters which are not readily accessible.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26006/1/0000073.pd

Sorption of hydrophobic compounds by sediments, soils and suspended solids--II. Sorbent evaluation studies

Concepts underlying the sorption of hydrophobic compounds and models for representation of observed equilibrium relationships were presented in Part I of this series. The earlier paper also summarized and evaluated major factors which affect the sorption of pollutants in natural environmental systems. This second part of the series presents a detailed summary and evaluation of the sorption of a particular class of hydrophobic pollutants, polychlorinated biphenyls (PCB), on a variety of different types of sediments, soils, suspended solids, and microorganisms. Equilibrium models described in Part I are used here to describe and analyze the PCB sorption data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25453/1/0000903.pd