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- Complexity and Approximability of the Maximum Flow Problem with Minimum Quantities (2012)
- We consider the maximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which may depend on the arc. This problem has recently been shown to be weakly NP-complete even on series-parallel graphs. In this paper, we provide further complexity and approximability results for MFPMQ and several special cases. We first show that it is strongly NP-hard to approximate MFPMQ on general graphs (and even bipartite graphs) within any positive factor. On series-parallel graphs, however, we present a pseudo-polynomial time dynamic programming algorithm for the problem. We then study the case that the minimum quantity is the same for each arc in the network and show that, under this restriction, the problem is still weakly NP-complete on general graphs, but can be solved in strongly polynomial time on series-parallel graphs. On general graphs, we present a \((2 - 1/\lambda) \)-approximation algorithm for this case, where \(\lambda\) denotes the common minimum quantity of all arcs.

- The Generalized Assignment Problem with Minimum Quantities (2012)
- We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (a minimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the most general version of the problem, we show that it does not admit a polynomial time approximation algorithm (unless P=NP), even for the case of a single bin. This motivates to study dual approximation algorithms that compute solutions violating the bin capacities and minimum quantities by a constant factor. When the number of bins is fixed and the minimum quantity of each bin is at least a factor \(\delta>1\) larger than the largest size of an item in the bin, we show how to obtain a polynomial time dual approximation algorithm that computes a solution violating the minimum quantities and bin capacities by at most a factor \(1-\frac{1}{\delta}\) and \(1+\frac{1}{\delta}\), respectively, and whose profit is at least as large as the profit of the best solution that satisfies the minimum quantities and bin capacities strictly. In particular, for \(\delta=2\), we obtain a polynomial time (1,2)-approximation algorithm.

- 100% Green Computing At The Wrong Location? (2012)
- Modern society relies on convenience services and mobile communication. Cloud computing is the current trend to make data and applications available at any time on every device. Data centers concentrate computation and storage at central locations, while they claim themselves green due to their optimized maintenance and increased energy efﬁciency. The key enabler for this evolution is the microelectronics industry. The trend to power efﬁcient mobile devices has forced this industry to change its design dogma to: ”keep data locally and reduce data communication whenever possible”. Therefore we ask: is cloud computing repeating the aberrations of its enabling industry?

- Homogeneous Penalizers and Constraints in Convex Image Restoration (2012)
- Recently convex optimization models were successfully applied for solving various problems in image analysis and restoration. In this paper, we are interested in relations between convex constrained optimization problems of the form \({\rm argmin} \{ \Phi(x)\) subject to \(\Psi(x) \le \tau \}\) and their penalized counterparts \({\rm argmin} \{\Phi(x) + \lambda \Psi(x)\}\). We recall general results on the topic by the help of an epigraphical projection. Then we deal with the special setting \(\Psi := \| L \cdot\|\) with \(L \in \mathbb{R}^{m,n}\) and \(\Phi := \varphi(H \cdot)\), where \(H \in \mathbb{R}^{n,n}\) and \(\varphi: \mathbb R^n \rightarrow \mathbb{R} \cup \{+\infty\} \) meet certain requirements which are often fulfilled in image processing models. In this case we prove by incorporating the dual problems that there exists a bijective function such that the solutions of the constrained problem coincide with those of the penalized problem if and only if \(\tau\) and \(\lambda\) are in the graph of this function. We illustrate the relation between \(\tau\) and \(\lambda\) for various problems arising in image processing. In particular, we point out the relation to the Pareto frontier for joint sparsity problems. We demonstrate the performance of the constrained model in restoration tasks of images corrupted by Poisson noise with the \(I\)-divergence as data fitting term \(\varphi\) and in inpainting models with the constrained nuclear norm. Such models can be useful if we have a priori knowledge on the image rather than on the noise level.

- AXI4-Stream Upsizing/Downsizing Data Width Converters for Hardware-In-the-Loop Simulations (2013)
- Hardware prototyping is an essential part in the hardware design flow. Furthermore, hardware prototyping usually relies on system-level design and hardware-in-the-loop simulations in order to develop, test and evaluate intellectual property cores. One common task in this process consist on interfacing cores with different port specifications. Data width conversion is used to overcome this issue. This work presents two open source hardware cores compliant with AXI4-Stream bus protocol, where each core performs upsizing/downsizing data width conversion.

- Ökonomische Auswirkungen und Imageeffekte des FCK für die Stadt Kaiserslautern (2014)
- Ökonomische Auswirkungen und Imageeffekte des FCK für die Stadt Kaiserslautern

- Stadtentwicklung Kaiserslautern (2014)
- Stadtentwicklung Kaiserslautern