Christian Schulz

Christian Schulz
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Christian Schulz

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Pub Categories

Computer Science - Data Structures and Algorithms (26)
Computer Science - Distributed; Parallel; and Cluster Computing (16)
Computer Science - Neural and Evolutionary Computing (7)
Mathematics - Combinatorics (3)
Physics - Physics and Society (2)
Computer Science - Digital Libraries (1)
Mathematics - Numerical Analysis (1)
Computer Science - Computational Geometry (1)
Computer Science - Computer Vision and Pattern Recognition (1)
Mathematics - Optimization and Control (1)
Computer Science - Graphics (1)

Publications Authored By Christian Schulz

Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in multiprocessor scheduling. We identified the additional constraint of acyclic dependencies between blocks when mapping computer vision and imaging applications to a heterogeneous embedded multiprocessor. Read More

This paper severs as a user guide to the mapping framework VieM (Vienna Mapping and Sparse Quadratic Assignment). We give a rough overview of the techniques used within the framework and describe the user interface as well as the file formats used. Read More

Communication and topology aware process mapping is a powerful approach to reduce communication time in parallel applications with known communication patterns on large, distributed memory systems. We address the problem as a quadratic assignment problem (QAP), and present algorithms to construct initial mappings of processes to processors as well as fast local search algorithms to further improve the mappings. By exploiting assumptions that typically hold for applications and modern supercomputer systems such as sparse communication patterns and hierarchically organized communication systems, we arrive at significantly more powerful algorithms for these special QAPs. Read More

We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that have previously been unsolved. Read More

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. Read More

We consider the notion of a signed magic array, which is an $m \times n$ rectangular array with the same number of filled cells $s$ in each row and the same number of filled cells $t$ in each column, filled with a certain set of numbers that is symmetric about the number zero, such that every row and column has a zero sum. We attempt to make progress toward a characterization of for which $(m, n, s, t)$ there exists such an array. This characterization is complete in the case where $n = s$ and in the case where $n = m$; we also characterize three-fourths of the cases where $n = 2m$. Read More

We explain how massive instances of scale-free graphs following the Barabasi-Albert model can be generated very quickly in an embarrassingly parallel way. This makes this popular model available for studying big data graph problems. As a demonstration, we generated a Petaedge graph in less than an hour. Read More

Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized sparse graphs, as well as high-quality independent sets in huge sparse graphs that are intractable for exact (exponential-time) algorithms. However, a major drawback of these algorithms is that they require significant preprocessing overhead, and therefore cannot be used to find a high-quality independent set quickly. Read More

We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time. Using several caching and lazy-evaluation techniques during coarsening and refinement, we reduce the running time by up to two-orders of magnitude compared to a naive $n$-level algorithm that would be adequate for ordinary graph partitioning. The overall performance is even better than the widely used hMetis hypergraph partitioner that uses a classical multilevel algorithm with few levels. Read More

A node separator of a graph is a subset S of the nodes such that removing S and its incident edges divides the graph into two disconnected components of about equal size. In this work, we introduce novel algorithms to find small node separators in large graphs. With focus on solution quality, we introduce novel flow-based local search algorithms which are integrated in a multilevel framework. Read More

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. Read More

Drawing large graphs appropriately is an important step for the visual analysis of data from real-world networks. Here we present a novel multilevel algorithm to compute a graph layout with respect to a recently proposed metric that combines layout stress and entropy. As opposed to previous work, we do not solve the linear systems of the maxent-stress metric with a typical numerical solver. Read More

We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time and thus allows very high quality. This includes a rating function that avoids nonuniform vertex weights, an efficient "semi-dynamic" hypergraph data structure, a very fast coarsening algorithm, and two new local search algorithms. One is a $k$-way hypergraph adaptation of Fiduccia-Mattheyses local search and gives high quality at reasonable cost. Read More

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. Read More

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. Read More

Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and overcome this gap both in theory and practice. The algorithms are multi-level generalizations of the known algorithms sample sort and multiway mergesort. Read More

In the SIGGRAPH 2014 paper [SvTSH14] an approach for animating deformable objects using sparse spacetime constraints is introduced. This report contains the proofs of two theorems presented in the paper. Read More

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. Read More

In this paper, we develop semi-external and external memory algorithms for graph partitioning and clustering problems. Graph partitioning and clustering are key tools for processing and analyzing large complex networks. We address both problems in the (semi-)external model by adapting the size-constrained label propagation technique. Read More

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. Read More

Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on large networks, multilevel methods are preferred in practice. Read More

We present a novel algorithm and validation method for disambiguating author names in very large bibliographic data sets and apply it to the full Web of Science (WoS) citation index. Our algorithm relies only upon the author and citation graphs available for the whole period covered by the WoS. A pair-wise publication similarity metric, which is based on common co-authors, self-citations, shared references and citations, is established to perform a two-step agglomerative clustering that first connects individual papers and then merges similar clusters. Read More

This paper serves as a user guide to the graph partitioning framework KaHIP (Karlsruhe High Quality Partitioning). We give a rough overview of the techniques used within the framework and describe the user interface as well as the file formats used. Moreover, we provide a short description of the current library functions provided within the framework. Read More

We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of computation, such as PRAM, External Memory, MapReduce and distributed memory models. Our CREW PRAM algorithm is the first O(log^2 n) time, linear work algorithm. Read More

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. Read More

The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing the multilevel partitioning frameworks has been on the refinement phase. Read More

We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs in a very short amount of time. Read More

We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from the multi-grid community. Local improvement algorithms are based max-flow min-cut computations and more localized FM searches. By combining these techniques, we obtain an algorithm that is fast on the one hand and on the other hand is able to improve the best known partitioning results for many inputs. Read More

We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning. We use the well known framework of multi-level graph partitioning. Read More