Adrian Neumann

NEFI: Network Extraction From Images.

Networks are amongst the central building blocks of many systems. Given a graph of a network, methods from graph theory enable a precise investigation of its properties. Software for the analysis of graphs is widely available and has been applied to study various types of networks. In some applications, graph acquisition is relatively simple. However, for many networks data collection relies on images where graph extraction requires domain-specific solutions. Here we introduce NEFI, a tool that extracts graphs from images of networks originating in various domains. Regarding previous work on graph extraction, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. NEFI provides a novel platform allowing practitioners to easily extract graphs from images by combining basic tools from image processing, computer vision and graph theory. Thus, NEFI constitutes an alternative to tedious manual graph extraction and special purpose tools. We anticipate NEFI to enable time-efficient collection of large datasets. The analysis of these novel datasets may open up the possibility to gain new insights into the structure and function of various networks. NEFI is open source and available at http://nefi.mpi-inf.mpg.de.

Certifying 3-Edge-Connectivity

We present a linear-time certifying algorithm that tests graphs for 3-edge-connectivity. If the input graph G is not 3-edge-connected, the algorithm returns a 2-edge-cut. If G is 3-edge-connected, the algorithm returns a construction sequence that constructs G from the graph with two nodes and three parallel edges using only operations that (obviously) preserve 3-edge-connectivity.

New Approximability Results for the Robust k-Median Problem

We consider a variant of the classical k-median problem, introduced by Anthony et al.[1]. In the Robust k-Median problem, we are given an n-vertex metric space (V,d) and m client sets \(\left\{ S_i \subseteq V \right\}_{i=1}^m\). We want to open a set F ⊆ V of k facilities such that the worst case connection cost over all client sets is minimized; that is, minimize \(\max_{i}\sum_{v \in S_i} d(F,v)\). Anthony et al. showed an O(logm) approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing Ω(logm/ loglogm) approximation hardness, unless \({\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})\). This result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.

Online checkpointing with improved worst-case guarantees

In the online checkpointing problem, the task is to continuously maintain a set of k checkpoints that allow to rewind an ongoing computation faster than by a full restart. The only operation allowed is to replace an old checkpoint by the current state. Our aim are checkpoint placement strategies that minimize rewinding cost, i.e., such that at all times T when requested to rewind to some time t≤T the number of computation steps that need to be redone to get to t from a checkpoint before t is as small as possible. In particular, we want that the closest checkpoint earlier than t is not further away from t than qk times the ideal distance T / (k+1), where qk is a small constant. Improving over earlier work showing 1+1/k≤qk≤2, we show that qk can be chosen asymptotically less than 2. We present algorithms with asymptotic discrepancy qk≤1.59+o(1) valid for all k and qk≤ln (4)+o(1)≤1.39+o(1) valid for k being a power of two. Experiments indicate the uniform bound pk≤1.7 for all k. For small k, we show how to use a linear programming approach to compute good checkpointing algorithms. This gives discrepancies of less than 1.55 for all k<60. We prove the first lower bound that is asymptotically more than one, namely qk≥1.30−o(1). We also show that optimal algorithms (yielding the infimum discrepancy) exist for all k.

On Efficiency and Reliability in Computer Science

Efficiency of algorithms and robustness against mistakes in their implementation or uncertainties in their input has always been of central interest in computer science. This thesis presents results for a number of problems related to this topic. Certifying algorithms enable reliable implementations by providing a certificate with their answer. A simple program can check the answers using the certificates. If the the checker accepts, the answer of the complex program is correct. The user only has to trust the simple checker. We present a novel certifying algorithm for 3-edgeconnectivity as well as a simplified certifying algorithm for 3-vertex-connectivity. Occasionally storing the state of computations, so called checkpointing, also helps with reliability since we can recover from errors without having to restart the computation. In this thesis we show how to do checkpointing with bounded memory and present several strategies to minimize the worst-case recomputation. In theory, the input for problems is accurate and well-defined. However, in practice it often contains uncertainties necessitating robust solutions. We consider a robust variant of the well known k-median problem, where the clients are grouped into sets. We want to minimize the connection cost of the expensive group. This solution is robust against which group we actually need to serve. We show that this problem is hard to approximate, even on the line, and evaluate heuristic solutions.