Optimal Algorithms for Online b-Matching with Variable Vertex Capacities

We study the b-matching problem, which generalizes classical online matching introduced by Karp, Vazirani and Vazirani (STOC 1990). Consider a bipartite graph G = (S ?? R,E). Every vertex s ? S is a server with a capacity b_s, indicating the number of possible matching partners. The vertices r ? R are requests that arrive online and must be matched immediately to an eligible server. The goal is to maximize the cardinality of the constructed matching. In contrast to earlier work, we study the general setting where servers may have arbitrary, individual capacities. We prove that the most natural and simple online algorithms achieve optimal competitive ratios. As for deterministic algorithms, we give a greedy algorithm RelativeBalance and analyze it by extending the primal-dual framework of Devanur, Jain and Kleinberg (SODA 2013). In the area of randomized algorithms we study the celebrated Ranking algorithm by Karp, Vazirani and Vazirani. We prove that the original Ranking strategy, simply picking a random permutation of the servers, achieves an optimal competitiveness of 1-1/e, independently of the server capacities. Hence it is not necessary to resort to a reduction, replacing every server s by b_s vertices of unit capacity and to then run Ranking on this graph with ?_{s ? S} b_s vertices on the left-hand side. From a theoretical point of view our result explores the power of randomization and strictly limits the amount of required randomness. From a practical point of view it leads to more efficient allocation algorithms. Technically, we show that the primal-dual framework of Devanur, Jain and Kleinberg cannot establish a competitiveness better than 1/2 for the original Ranking algorithm, choosing a permutation of the servers. Therefore, we formulate a new configuration LP for the b-matching problem and then conduct a primal-dual analysis. We extend this analysis approach to the vertex-weighted b-matching problem. Specifically, we show that the algorithm PerturbedGreedy by Aggarwal, Goel, Karande and Mehta (SODA 2011), again with a sole randomization over the set of servers, is (1-1/e)-competitive. Together with recent work by Huang and Zhang (STOC 2020), our results demonstrate that configuration LPs can be strictly stronger than standard LPs in the analysis of more complex matching problems

Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities

We study the b-matching problem in bipartite graphs G = (S,R,E). Each vertex s ? S is a server with individual capacity b_s. The vertices r ? R are requests that arrive online and must be assigned instantly to an eligible server. The goal is to maximize the size of the constructed matching. We assume that G is a (k,d)-graph [J. Naor and D. Wajc, 2018], where k specifies a lower bound on the degree of each server and d is an upper bound on the degree of each request. This setting models matching problems in timely applications. We present tight upper and lower bounds on the performance of deterministic online algorithms. In particular, we develop a new online algorithm via a primal-dual analysis. The optimal competitive ratio tends to 1, for arbitrary k ? d, as the server capacities increase. Hence, nearly optimal solutions can be computed online. Our results also hold for the vertex-weighted problem extension, and thus for AdWords and auction problems in which each bidder issues individual, equally valued bids. Our bounds improve the previous best competitive ratios. The asymptotic competitiveness of 1 is a significant improvement over the previous factor of 1-1/e^{k/d}, for the interesting range where k/d ? 1 is small. Recall that 1-1/e ? 0.63. Matching problems that admit a competitive ratio arbitrarily close to 1 are rare. Prior results rely on randomization or probabilistic input models

Tight Bounds for Online Coloring of Basic Graph Classes

We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our bounds also hold for randomized online algorithms, for which hardly any results were known. Technically, we construct lower bounds for chordal graphs. The constructions then allow us to derive results on the performance of randomized online algorithms for the following further graph classes: trees, planar, bipartite, inductive, bounded-treewidth and disk graphs. It shows that the best competitive ratio of both deterministic and randomized online algorithms is Theta(log n), where n is the number of vertices of a graph. Furthermore, we prove that this guarantee cannot be improved if an online algorithm has a lookahead of size O(n/log n) or access to a reordering buffer of size n^(1-epsilon), for any 0 < epsilon <= 1. A consequence of our results is that, for all of the above mentioned graph classes except bipartite graphs, the natural First Fit coloring algorithm achieves an optimal performance, up to constant factors, among deterministic and randomized online algorithms

A COMPETENCE PORTFOLIO FOR FUTURE LEADERS IN ADVANCED SYSTEMS ENGINEERING

Due to the increasing importance of advanced systems, whose development calls for interdisciplinary and integrative approaches, and fundamental changes in the work environment, leaders are required to have a wide range of competences. Therefore, the aim of this work is to identify competences of future leaders, that are specifically relevant in Advanced Systems Engineering (ASE). Thus, professional, social, methodological, and self competences developed by a literature review are validated through expert interviews and prioritized by a survey. The insights are then presented in a competence portfolio including 30 areas of competences. The portfolio consists of areas of competence that are either relevant in the context of ASE (e.g. intercultural and interdisciplinary competence), New Work (e.g. competence to empower employees) or are relevant to leaders in general. It was possible to add further aspects that are necessary in ASE to the aspects from the literature review. The experts interviewed emphasized various aspects of interdisciplinary work and made clear that in future, leaders should place their employees at the heart of their activities and empower them according to their strengths and weaknesses

Improving distributed collaboration at Porsche Engineering Services GmbH through the application of the EDiT Method

To support development teams with their individual challenges of distributed collaboration in product development, the EDiT method is being developed. This paper contributes to the continuous validation of the EDiT method by a field study at the process team of Porsche Engineering Services GmbH to support the successful transfer into practice. The validation is based on validation by application, validation by evaluation of the contribution to success, and validation by comparison of the requirements. The contribution of the EDiT method could be proven by different measurement criteria, e.g. reducing the average number of days to finish a task by a remarkable amount

MODELLING TECHNICAL SYSTEMS IN THE EARLY PHASE: PROPOSING A FORMAL DEFINITION FOR THE SYSTEM CONCEPT

The task of developing “concepts” is common in all fields of engineering, especially in the early phases of product development. However, an in-depth literature analysis showed that authors - often depending on different contexts in design research, education, and industry - define the term “concept” in differing ways. The aspect of reference-based development is rarely addressed in existing definitions. This indicates that there is a need for an updated and concise concept definition. In this paper, the authors propose a new definition of the term “system concept” within the context of SGE - System Generation Engineering that incorporates the findings from the literature analysis. The definition was reflected on in two case-studies. The first one contained the system concept for automotive display and operating systems, the second one the system concept for a kinesthetic-haptic VR interface. The proposed definition contains the relevant characteristics identified from the literature review and supports both current activity-based process models and reference-based development, as practical application has shown

Evaluation of Laminaria digitata and Phragmites australis for biogas production and nutrient recycling

Eutrophication and climate change are major global problems. The sea weed Laminaria digitata and the reed Phragmites australis have the potential to absorb nutrients and CO2 during growth, as well as being a source of renewable energy in the form of biogas. The aim of this study was to evaluate Laminaria digitata and Phragmites australis concerning biogas production and nutrient recycling using a two-stage pilot scale process. The plant has a total volume of 430 L and consists of a hydrolysis bed and an up-flow anaerobic sludge blanket reactor (UASB). Two experiments were performed; one with Laminaria digitata as the sole substrate and one with a mixture of Laminaria digitata and Phragmites australis. Frozen substrates were placed in the hydrolysis bed and digestion was performed at 305 K during 70 days for Laminaria digitata and 100 days for the mixture of Laminaria digitata and Phragmites australis. The methane yield achieved was approximately 170 L kg−1 volatile substances (273.15 K, 101.3 kPa) in both experiments. These results suggest that Laminaria digitata can be efficiently digested in larger scale and has the potential to contribute to a future sustainable energy mix, considering its relatively high methane yield when anaerobically digested as the sole substrate. Digestion of Phragmites australis needs further development to make use of its full potential

A meta-analysis

There is a lack of predictive biomarkers that can identify patients with head and neck squamous cell carcinoma (HNSCC) who will experience treatment failure and develop drug resistance, recurrence, and metastases. Cancer stem-like cells (CSC) were identified as a subset of cells within the tumor in a variety of solid tumors including HNSCC. CSC are considered the tumor-initiating population responsible for recurrence or metastasis and are associated with therapy resistance. This meta-analysis including fourteen studies with altogether 1258 patients updates and summarizes all relevant data on the impact of ALDH1+ CSC on the prognosis of HNSCC and its association with clinicopathological parameters. ALDH1 expression is highly correlated with tumor differentiation (G3 vs. G1+G2; odds ratio = 2.85. 95% CI: 1.72–4.73, P<0.0001) and decreased overall survival (relative risk = 1.77. 95% CI: 1.41–2.22, P<0.0001) if one out of seven studies was excluded because of heterogeneity. These findings provide insights into the understanding of more aggressive tumor phenotypes and also suggest that the prognostic value provided by HNSCC-subtyping by CSC frequency warrant further clinical investigation

Introducing and Implementing the Allpairs Skeleton for Programming Multi-GPU Systems

Algorithmic skeletons simplify software development: they abstract typical patterns of parallelism and provide their efficient implementations, allowing the application developer to focus on the structure of algorithms, rather than on implementation details. This becomes especially important for modern parallel systems with multiple graphics processing units (GPUs) whose programming is complex and error-prone, because state-of-the-art programming approaches like CUDA and OpenCL lack high-level abstractions. We define a new algorithmic skeleton for allpairs computations which occur in real-world applications, ranging from bioinformatics to physics. We develop the skeleton’s generic parallel implementation for multi-GPU Systems in OpenCL. To enable the automatic use of the fast GPU memory, we identify and implement an optimized version of the allpairs skeleton with a customizing function that follows a certain memory access pattern. We use matrix multiplication as an application study for the allpairs skeleton and its two implementations and demonstrate that the skeleton greatly simplifies programming, saving up to 90 % of lines of code as compared to OpenCL. The performance of our optimized implementation is up to 6.8 times higher as compared with the generic implementation and is competitive to the performance of a manually written optimized OpenCL code