Uniform unweighted set cover: The power of non-oblivious local search

We are given $n$ base elements and a finite collection of subsets of them. The size of any subset varies between $p$ to $k$ ($p<k$). In addition, we assume that the input contains all possible subsets of size $p$. Our objective is to find a subcollection of minimum-cardinality which covers all the elements. This problem is known to be NP-hard. We provide two approximation algorithms for it, one for the generic case, and an improved one for the special case of $(p,k)=(2,4)$.The algorithm for the generic case is a greedy one, based on packing phases: at each phase we pick a collection of disjoint subsets covering $i$ new elements, starting from $i=k$ down to $i=p+1$. At a final step we cover the remaining base elements by the subsets of size $p$. We derive the exact performance guarantee of this algorithm for all values of $k$ and $p$, which is less than $H_k$, where $H_k$ is the $k$’th harmonic number. However, the algorithm exhibits the known improvement methods over the greedy one for the unweighted $k$-set cover problem (in which subset sizes are only restricted not to exceed $k$), and hence it serves as a benchmark for our improved algorithm.The improved algorithm for the special case of $(p,k)=(2,4)$ is based on non-oblivious local search: it starts with a feasible cover, and then repeatedly tries to replace sets of size 3 and 4 so as to maximize an objective function which prefers big sets over small ones. For this case, our generic algorithm achieves an asymptotic approximation ratio of $1.5+?$, and the local search algorithm achieves a better ratio, which is bounded by $1.458333\dots +?$.     

Wasserhaushalt kleiner Grundwassereinzugsgebiete im Südosten Berlins

The water management in Berlin leads to a situation, where nearly the entire groundwater balance is affected by human activities. Sealing, discharge by water plants and factories, drainage and leaky pipes are only some examples for the human influence. In the southeast of Berlin the Free University carries out a research project on the water balance of an almost natural catchment area. The investigations refer to the groundwater recharge in a forest and in small moist biotopes. A quantitative relation between the water level and the climatic water balance in the catchment area could be found by stochastic methods. The water balance equation was used to construct the graph of the weekly groundwater recharge in a moist biotope and in a forest.     

Effects of cereals and culture filtrate ofTrichoderma viride on lipid metabolism of swine

Swine were fed corn-or barley-based diets with, or without, culture filtrate (CF) ofTrichoderma viride for 21 days. Weight gains were nonsignificantly but slightly increased by CF. The activities of β-hydroxy-β-methylglutaryl coenzyme A (HMG-CoA) reductase, cholesterol 7α-hydroxylase, acetyl-CoA carboxylase (ACX), fatty acid synthetase (FAS) and other lipogenic enzymes in several tissues were determined. Significant decreases in the activities of HMG-CoA reductase and cholesterol 7α-hydroxylase in all tissues of swine fed the CF-diets were observed. The major site for the regulation of cholesterol biosynthesis was adipose tissue followed by the intestine, liver, lung and muscle in order of activity The concentrations of cholesterol in serum and muscle were decreased 27% and 23%, respectively, by CF. ACX and FAS activities increased ca. 2-fold when CF was fed with either of the cereal-based diets. The major sites for fatty acid synthesis was the adipose tissue and, to a lesser extent, the liver. Very low rates of synthesis were detected in intestine, lung and muscle. Similar distributions of activities were found for related lipogenic enzymes. Cooperative investigation between the Science and Education Administration, US Department of Agriculture, and College of Agricultural and Life Sciences, University of Wisconsin, Madison. Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the US Department of Agriculture and does not imply its approval to the exclusion of other products that may also be suitable.     

Effects of different fractions of the barley kernel on the hepatic lipid metabolism of chickens

Various physical fractions of the barley kernel were fed to one-day-old female and male chickens to determine their effect on hepatic β-hydroxy-β-methylglutaryl coenzyme A (HMG-CoA) reductase, cholesterol 7α-hydroxylase and the lipogenic enzymes, acetyl-CoA carboxylase (ACX), malic enzyme (ME), citrate-cleavage enzyme (CCE) and fatty acid synthetase (FAS) at the subcellular level. Significant inhibition (p<0.01) of cholesterol biosynthesis accompanied by significant decreases in plasma cholesterol concentrations and induction of fatty acid synthesis were found in diets based on pearled barley, barley pearlings and a high-protein barley flour (HPBF: aleurone and subaleurone layers of barley endosperm) separated from the pearlings when compared to corn. Lower weight gains in 1- to 4-week-old birds fed the high-protein barley flour were found to be the result of lower feed consumption; pair feeding of 12-week-old birds with diets based on corn and high-protein barley flour produced equal weight gains in both treatments and significant reductions in hepatic HMG-CoA reductase, plasma cholesterol and induction in several lipogenic enzymes in birds fed the high-protein barley flour. Substitutions of 5–20% high-protein barley flour for corn in a corn-based diet produced significant weight gains (p<0.01) of 10 to 20% in 2-week-old chickens, inhibited cholesterol biosynthesis by 45–65% and produced a 3-fold increase in a fatty acid synthetase. The results indicate that HPBF contains an inhibitor(s) of cholesterol biosynthesis and a growth factor(s) when compared to a corn-based diet. Cooperative investigation between the Science and Education Administration, US Department of Agriculture, and the College of Agricultural and Life Sciences, University of Wisconsin-Madison. Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the US Department of Agriculture and does not imply its approval to the exclusion of other products that may also be suitable.     

Infiltration and dimensional scaling of inkjet droplets on thick isotropic porous materials

We study the imbibition of picoliter (pL)-sized inkjet droplets on controlled pore glass membranes (CPG), as a suitable model for isotropic three-dimensional porous materials. We do so using a variety of liquids, i.e., water, formamide and diiodomethane, and measure the evolution of the imbibition process using high-speed digital imaging. Here, experiments were conducted on 2–280 nm CPG membranes with drops with initial volumes ranging from 100 to 600 pL. We derive scaling laws for imbibition through dimensional analysis and advance the argument that the rate of absorption is related to two-dimensionless groups \(V = v(t) \epsilon /v_{\text{tot}} ;\,T = tkp_{\text{c}} /\mu \,\left( { \epsilon /v_{\text{tot}} } \right)^{2/3} ,\) where v(t) is the imbibed volume, as determined from experiments, t is the time, v _tot the total liquid volume, \( \epsilon \) the porosity, μ the liquid viscosity, k the permeability, and p _c the Laplace capillary pressure. We show this scaling to well describe the system at intermediate T values and report that \(V \propto T^{0.8} .\)      

How to allocate review tasks for robust ranking

In the process of reviewing and ranking projects by a group of reviewers, the allocation of the subset of projects to each reviewer has major impact on the robustness of the outcome ranking. We address here this problem where each reviewer is assigned, out of the list of all projects, a subset of up to k projects. Each individual reviewer then ranks and compares all pairs of k projects. The k-allocation problem is to determine an allocation of up to k projects to each reviewer, that lie within the expertise set of the reviewer, so that the resulting union of reviewed projects has certain desirable properties. The k-complete problem is a k-allocation with the property that all pairs of projects have been compared by at least one reviewer. A k-complete allocation is desirable as otherwise there may be projects that were not compared by any reviewer, leading to possible adverse properties in the outcome ranking. When a k-complete allocation cannot be achieved, one might settle for other properties. One basic requirement is that each pair of projects is comparable via a ranking path which is a sequence of pairwise rankings of projects implying a comparison of all pairs on the path. A k-allocation with a ranking path between each pair is the connectivity-k-aloc. Since the robustness of relative comparisons deteriorates with increased length of the ranking path, another goal is that between each pair of projects there will be at least one ranking path that has at most two hops or q hops for fixed values of q. An alternative means for increasing the robustness of the ranking is to use a k-allocation with at least p disjoint ranking paths between each pair. We model all these problems as graph problems. We demonstrate that the connectivity-k-aloc problem is polynomially solvable, using matroid intersection; we prove that the k-complete problem is NP-hard unless k = 2; and we provide approximation algorithms for a related optimization problem. All other variants are shown to be NP-complete for all values of k ≥ 2.     

Variable Sized Online Interval Coloring with Bandwidth

We consider online coloring of intervals with bandwidth in a setting where colors have variable capacities. Whenever the algorithm opens a new color, it must choose the capacity for that color and cannot change it later. A set of intervals can be assigned the same color a of capacity C _a if the sum of bandwidths of intervals at each point does not exceed C _a . The goal is to minimize the total capacity of all the colors used. We consider the bounded model, where all capacities must be chosen in the range (0,1], and the unbounded model, where the algorithm may use colors of any positive capacity. For the absolute competitive ratio, we give an upper bound of 14 and a lower bound of 4.59 for the bounded model, and an upper bound of 4 and a matching lower bound of 4 for the unbounded model. We also consider the offline version of these problems and show that whereas the unbounded model is polynomially solvable, the bounded model is NP-hard in the strong sense and admits a 3.6-approximation algorithm. A preliminary version of this paper has appeared in the Proceedings of the 10th Scandinavian Workshop on Algorithm Theory (SWAT 2006), Lecture Notes in Computer Science, Vol. 4059, pp. 29–40, Springer, 2006.     

Amit - the situation manager

This paper presents the situation manager, a tool that includes both a language and an efficient runtime execution mechanism aimed at reducing the complexity of active applications. This tool follows the observation that in many cases there is a gap between current tools that enable one to react to a single event (following the ECA: event-condition-action paradigm) and the reality in which a single event may not require any reaction; however, the reaction should be given to patterns over the event history.The concept of situation presented in this paper extends the concept of composite event in its expressive power, flexibility, and usability. This paper motivates the work, surveys other efforts in this area, and discusses both the language and the execution model.Received: 6 February 2002, Accepted: 20 May 2003, Published online: 30 September 2003Edited by: K. Ramamritham