Peter Sanders

Ümit V. Çatalyürek, Karen D. Devine, Marcelo Fonseca Faraj et al.

In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together with future research directions. Our work serves as an update to a previous survey on the topic. In particular, the survey extends the previous survey by also covering hypergraph partitioning and streaming algorithms, and has an additional focus on parallel algorithms.

Moritz Laupichler, Robin Andre, Kim Kandler et al.

In ride-pooling, a fleet of vehicles is dynamically dispatched to bring travelers from A to B, trying to pool riders with similar itineraries to improve the use of resources compared to taxis or private cars. Ride-pooling is considered a core building block of future transport systems with autonomous vehicles. In this paper, we introduce Mt-KaRRi, a novel dispatcher for dynamic ride-pooling that leverages state-of-the-art shortest-path algorithms to process millions of travelers per hour. We add a simple mode choice model and use realistic travel demand in three different urban areas for extensive experiments. We find that our dispatcher scales well with a response time per request of around 1ms even for our largest instances. We show how this scalability can be used to conduct ride-pooling studies at unprecedented scale. For instance, we determine how the quality of rides and usage of vehicle resources develop for tens of thousands of vehicles and millions of travelers. We envision Mt-KaRRi as a tool for future ride-pooling simulation studies at scale.

Bernhard Beckert, Timo Bingmann, Moritz Kiefer et al.

MapReduce frameworks are widely used for the implementation of distributed algorithms. However, translating imperative algorithms into these frameworks requires significant structural changes to the algorithm. As the costs of running faulty algorithms at scale can be severe, it is highly desirable to verify the correctness of the translation, i.e., to prove that the MapReduce version is equivalent to the imperative original. We present a novel approach for proving equivalence between imperative and MapReduce algorithms based on partitioning the equivalence proof into a sequence of equivalence proofs between intermediate programs with smaller differences. Our approach is based on the insight that two kinds of sub-proofs are required: (1) uniform transformations changing the controlflow structure that are mostly independent of the particular context in which they are applied; and (2) context-dependent transformations that are not uniform but that preserve the overall structure and can be proved correct using coupling invariants. We demonstrate the feasibility of our approach by evaluating it on two prototypical algorithms commonly used as examples in MapReduce frameworks: k-means and PageRank. To carry out the proofs, we use the interactive theorem prover Coq with partial proof automation. The results show that our approach and its prototypical implementation based on Coq enables equivalence proofs of non-trivial algorithms and could be automated to a large degree.

Julian Arz, Peter Sanders, Johannes Stegmaier et al.

Cell nuclei segmentation is one of the most important tasks in the analysis of biomedical images. With ever-growing sizes and amounts of three-dimensional images to be processed, there is a need for better and faster segmentation methods. Graph-based image segmentation has seen a rise in popularity in recent years, but is seen as very costly with regard to computational demand. We propose a new segmentation algorithm which overcomes these limitations. Our method uses recursive balanced graph partitioning to segment foreground components of a fast and efficient binarization. We construct a model for the cell nuclei to guide the partitioning process. Our algorithm is compared to other state-of-the-art segmentation algorithms in an experimental evaluation on two sets of realistically simulated inputs. Our method is faster, has similar or better quality and an acceptable memory overhead.

Peter Sanders, Christian Schulz, Darren Strash et al.

Computing high quality node separators in large graphs is necessary for a variety of applications, ranging from divide-and-conquer algorithms to VLSI design. In this work, we present a novel distributed evolutionary algorithm tackling the k-way node separator problem. A key component of our contribution includes new k-way local search algorithms based on maximum flows. We combine our local search with a multilevel approach to compute an initial population for our evolutionary algorithm, and further show how to modify the coarsening stage of our multilevel algorithm to create effective combine and mutation operations. Lastly, we combine these techniques with a scalable communication protocol, producing a system that is able to compute high quality solutions in a short amount of time. Our experiments against competing algorithms show that our advanced evolutionary algorithm computes the best result on 94% of the chosen benchmark instances.

Johannes Stegmaier, Julian Arz, Benjamin Schott et al.

Systematic validation is an essential part of algorithm development. The enormous dataset sizes and the complexity observed in many recent time-resolved 3D fluorescence microscopy imaging experiments, however, prohibit a comprehensive manual ground truth generation. Moreover, existing simulated benchmarks in this field are often too simple or too specialized to sufficiently validate the observed image analysis problems. We present a new semi-synthetic approach to generate realistic 3D+t benchmarks that combines challenging cellular movement dynamics of real embryos with simulated fluorescent nuclei and artificial image distortions including various parametrizable options like cell numbers, acquisition deficiencies or multiview simulations. We successfully applied the approach to simulate the development of a zebrafish embryo with thousands of cells over 14 hours of its early existence.

Sebastian Lamm, Peter Sanders, Christian Schulz et al.

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space---which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.

Nitin Ahuja, Matthias Bender, Peter Sanders et al.

Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often include a reasonable balance, compact form, contiguity and small average journey times which are usually encoded in the objective function or formulated as constraints. We address the territory design problem by developing graph theoretic models that also consider the underlying road network. The derived graph models enable us to tackle the territory design problem by modifying graph partitioning algorithms and mixed integer programming formulations so that the objective of the planning problem is taken into account. We test and compare the algorithms on several real world instances.

Thomas Leibfried, Tamara Mchedlidze, Nico Meyer-Hübner et al.

Future power grids will offer enhanced controllability due to the increased availability of power flow control units (FACTS). As the installation of control units in the grid is an expensive investment, we are interested in using few controllers to achieve high controllability. In particular, two questions arise: How many flow control buses are necessary to obtain globally optimal power flows? And if fewer flow control buses are available, what can we achieve with them? Using steady state IEEE benchmark data sets, we explore experimentally that already a small number of controllers placed at certain grid buses suffices to achieve globally optimal power flows. We present a graph-theoretic explanation for this behavior. To answer the second question we perform a set of experiments that explore the existence and costs of feasible power flow solutions at increased loads with respect to the number of flow control buses in the grid. We observe that adding a small number of flow control buses reduces the flow costs and extends the existence of feasible solutions at increased load.

Sebastian Lamm, Peter Sanders, Christian Schulz

Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations based on graph partitioning and local search algorithms. More precisely, we employ a state-of-the-art graph partitioner to derive operations that enable us to quickly exchange whole blocks of given independent sets. To enhance newly computed offsprings we combine our operators with a local search algorithm. Our experimental evaluation indicates that we are able to outperform state-of-the-art algorithms on a variety of instances.

Jonathan Dimond, Peter Sanders

We show how full-text search based on inverted indices can be accelerated by clustering the documents without losing results (SeCluD -- SEarch with CLUstered Documents). We develop a fast multilevel clustering algorithm that explicitly uses query cost for conjunctive queries as an objective function. Depending on the inputs we get up to four times faster than non-clustered search. The resulting clusters are also useful for data compression and for distributing the work over many machines.

Henning Meyerhenke, Peter Sanders, Christian Schulz

Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for these networks. This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsened graph. The resulting system is both more scalable and achieves higher quality than state-of-the-art systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. For example, our algorithm can partition a web graph with 3.3 billion edges in less than sixteen seconds using 512 cores of a high performance cluster while producing a high quality partition -- none of the competing systems can handle this graph on our system.

Peter Sanders, Christian Schulz

We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these searches maintaining balance by applying a negative cycle detection algorithm. We combine this technique with an algorithm to balance unbalanced solutions and integrate it into a parallel multi-level evolutionary algorithm, KaFFPaE, to tackle the problem. Overall, we obtain a system that is fast on the one hand and on the other hand is able to improve or reproduce most of the best known perfectly balanced partitioning results ever reported in the literature.