Improved Online Algorithms for Knapsack and GAP in the Random Order Model

The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the online setting, items are revealed one by one and the decision, if the current item is packed or discarded forever, must be done immediately and irrevocably upon arrival. We study the online variant in the random order model where the input sequence is a uniform random permutation of the item set. We develop a randomized (1/6.65)-competitive algorithm for this problem, outperforming the current best algorithm of competitive ratio 1/8.06 [Kesselheim et al. SIAM J. Comp. 47(5)]. Our algorithm is based on two new insights: We introduce a novel algorithmic approach that employs two given algorithms, optimized for restricted item classes, sequentially on the input sequence. In addition, we study and exploit the relationship of the knapsack problem to the 2-secretary problem. The generalized assignment problem (GAP) includes, besides the knapsack problem, several important problems related to scheduling and matching. We show that in the same online setting, applying the proposed sequential approach yields a (1/6.99)-competitive randomized algorithm for GAP. Again, our proposed algorithm outperforms the current best result of competitive ratio 1/8.06 [Kesselheim et al. SIAM J. Comp. 47(5)]

New Results for the k-Secretary Problem

Suppose that n numbers arrive online in random order and the goal is to select k of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing future items. This problem is known as the k-secretary problem, which includes the classical secretary problem with the special case k=1. It is well-known that the latter problem can be solved by a simple algorithm of competitive ratio 1/e which is asymptotically optimal. When k is small, only for k=2 does there exist an algorithm beating the threshold of 1/e [Chan et al. SODA 2015]. The algorithm relies on an involved selection policy. Moreover, there exist results when k is large [Kleinberg SODA 2005]. In this paper we present results for the k-secretary problem, considering the interesting and relevant case that k is small. We focus on simple selection algorithms, accompanied by combinatorial analyses. As a main contribution we propose a natural deterministic algorithm designed to have competitive ratios strictly greater than 1/e for small k >= 2. This algorithm is hardly more complex than the elegant strategy for the classical secretary problem, optimal for k=1, and works for all k >= 1. We explicitly compute its competitive ratios for 2 <= k <= 100, ranging from 0.41 for k=2 to 0.75 for k=100. Moreover, we show that an algorithm proposed by Babaioff et al. [APPROX 2007] has a competitive ratio of 0.4168 for k=2, implying that the previous analysis was not tight. Our analysis reveals a surprising combinatorial property of this algorithm, which might be helpful for a tight analysis of this algorithm for general k

Subventionen im Luftverkehr

Im Luftverkehr wiesen in den vergangenen Jahrzehnten sowohl die Passagierzahlen als auch das Frachtaufkommen überdurchschnittliche Wachstumsraten auf. Hiervon haben Fluggesellschaften, Flughäfen und Flugzeugindustrie profitiert. Es ist zu erwarten, dass sich der Luftverkehr von den Einbrüchen in den beiden vergangenen Jahren - zurückzuführen auf die Terroranschläge vom 11. September 2001, die Lungenkrankheit SARS, den Irak-Krieg sowie eine generelle Wirtschaftsschwäche - bald wieder erholt. Unabhängig von der stark wachsenden Nachfrage nach Luftverkehrsleistungen wird der Luftfahrtsektor in vielfältiger Weise subventioniert. Dies ist das Ergebnis einer Studie, die im Auftrag des Umweltbundesamtes durchgeführt wurde. Die Bundesregierung hält zwar einen umfassenden Subventionsabbau selbst für dringend nötig, doch sind diesem in der Luftfahrt enge Grenzen gesetzt. Dazu ist dieser Bereich zu sehr in internationale Abkommen und Regelwerke eingebettet

Elevated level of cell-free plasma DNA is associated with breast cancer

Background: We analysed cell-free DNA (cfDNA) in the plasma of patients with both malignant and benign breast lesions by real-time quantitative PCR to determine whether the finding may have diagnostic and prognostic implications. Methods: Plasma samples were obtained from 33 patients with breast cancer, 32 patients with benign breast lesions and 50 healthy women as normal controls. Circulatory cfDNA was extracted from the plasma samples and quantified by real-time quantitative PCR for the glyceraldehyde-3-phosphate dehydrogenase (GAPDH) gene. Results: The mean concentrations of cfDNA in the plasma samples from patients with breast cancer, patients with benign breast lesions and normal controls were 2,285, 1,368 and 1,489 genome equivalents (GE) per millilitre, respectively. The level of cfDNA in the breast cancer group was significantly higher than those in the benign lesion group and control group (P=0.007 and 0.013, respectively). These findings were associated with malignant tumour size. The levels of the cfDNA were high in patients with lymph node involvement and distant metastasis. Conclusions: Our results suggest that levels of cfDNA in the plasma are elevated in malignant breast cancer and correlated with tumour size. These findings could have diagnostic and prognostic value for malignant breast tumour

Online Strip Packing with Polynomial Migration

We consider the relaxed online strip packing problem, where rectangular items arrive online and have to be packed into a strip of fixed width such that the packing height is minimized. Thereby, repacking of previously packed items is allowed. The amount of repacking is measured by the migration factor, defined as the total size of repacked items divided by the size of the arriving item. First, we show that no algorithm with constant migration factor can produce solutions with asymptotic ratio better than 4/3. Against this background, we allow amortized migration, i.e. to save migration for a later time step. As a main result, we present an AFPTAS with asymptotic ratio 1 + O(epsilon) for any epsilon > 0 and amortized migration factor polynomial in 1/epsilon. To our best knowledge, this is the first algorithm for online strip packing considered in a repacking model

Nanocomposite Nafion-Silica membranes for direct methanol fuel cells

Commercially available proton exchange membranes such as Nafion do not meet the requirements for high power density direct methanol fuel cells, partly due to their high methanol permeability. The aim of this work is to develop a new class of high-proton conductivity membranes, with thermal and mechanical stability similar to Nafion and reduced methanol permeability. Nanocomposite membranes were produced by the in-situ sol-gel synthesis of silicon dioxide particles in preformed Nafion membranes. Microstructural modification of Nafion membranes with silica nanoparticles was shown in this work to reduce methanol crossover from 7.48x10-6 cm2s^-1 for pure Nafion® to 2.86 x10-6 cm2s^-1 for nanocomposite nafion membranes (Methanol 50% (v/v) solution, 75 degrees C). Best results were achieved with a silica composition of 2.6% (w/w). We propose that silica inhibits the conduction of methanol through Nafion by blocking sites necessary for methanol diffusion through the polymer electrolyte membrane. Effects of surface chemistry, nanoparticle formation and interactions with Nafion matrix are further addressed

Co-delivery of siRNAs and anti-cancer drugs using layered double hydroxide nanoparticles

In this research we employed layered double hydroxide nanoparticles (LDHs) to simultaneously deliver an anticancer drug 5-fluorouracil (5-FU) and Allstars Cell Death siRNA (CD-siRNA) for effective cancer treatment. The strategy takes advantage of the LDH anion exchange capacity to intercalate 5-FU into its interlayer spacing and load siRNA on the surface of LDH nanoparticles. LDH nanoparticles have been previously demonstrated as an effective cellular delivery system for 5-FU and siRNA separately in various investigations. More excitedly, the combination of CD-siRNA and anticancer drug 5-FU with the same LDH particles significantly enhanced cytotoxicity to three cancer cell lines, e.g. MCF-7, U2OS and HCT-116, compared to the single treatment with either CD-siRNA or 5-FU. This enhancement is probably a result of coordinate mitochondrial damage process. Thus, the strategy to co-deliver siRNA and an anticancer drug by LDHs has great potential to overcome the drug resistance and enhance cancer treatment

Preparation of new composite membranes for water desalination using electrodialysis

The use of polyethersulfone (PES), an excellent but highly hydrophobic thermoplastic, as a matrix material for ion-exchange membranes was investigated. To make PES ion-exchangeable, sulfonate groups were introduced to the polymer chains by sulfonation reaction with chlorosulfonic acid. The degree of sulfonation of sPES was estimated to be 21%. Preliminary experiments investigated the effect of polyethylene glycol (PEG) and Pluronic F127 as fillers to improve the hydrophilicity of the membranes. Moreover, a lab scale electrodialysis cell has been designed and set up to evaluate the performance of these novel membranes compared to the benchmark of commercial membranes. The results show promising properties of ion-exchange capacity, water uptake, conductivity and hydophilicity from blended membranes, comparable to commercial membranes, though the performance of the prepared membranes did not exceed the commercial one. Further characterization of the transport properties of ion-exchange membranes need to be investigated to be able to understand the effects of the fillers on the performance of the membranes in ED application