Ulrich Meyer

Bio: Ulrich Meyer is an academic researcher from Goethe University Frankfurt. The author has contributed to research in topics: Shortest path problem & Time complexity. The author has an hindex of 27, co-authored 137 publications receiving 3036 citations. Previous affiliations of Ulrich Meyer include Max Planck Society.

Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths

Abstract: We present improved cache-oblivious data structures and algorithms for breadth-first search (BFS) on undirected graphs and the single-source shortest path (SSSP) problem on undirected graphs with non-negative edge weights. For the SSSP problem, our result closes the performance gap between the currently best cache-aware algorithm and the cache-oblivious counterpart. Our cache-oblivious SSSP-algorithm takes nearly full advantage of block transfers for dense graphs. The algorithm relies on a new data structure, called bucket heap , which is the first cache-oblivious priority queue to efficiently support a weak D ECREASE K EY operation. For the BFS problem, we reduce the number of I/Os for sparse graphs by a factor of nearly sqrt{B}, where B is the cache-block size, nearly closing the performance gap between the currently best cache-aware and cache-oblivious algorithms.

External Memory Algorithms for Diameter and All-Pairs Shortest-Paths on Sparse Graphs

Abstract: We develop I/O-efficient algorithms for diameter and all-pairs shortest-paths (APSP). For general undirected graphs G(V,E) with non-negative edge weights and E/V = o(B/ log V) our approaches are the first to achieve o(V 2) I/Os. We also show that for unweighted undirected graphs, APSP can be solved with just \(O(V \cdot \textrm{sort}(E))\) I/Os. Both our weighted and unweighted approaches require O(V 2) space. For diameter computations we provide I/O-space tradeoffs. Finally, we provide improved results for both diameter and APSP computation on directed planar graphs.

Randomized external-memory algorithms for line segment intersection and other geometric problems

Abstract: We show that the well-known random incremental construction of Clarkson and Shor18 can be adapted to provide efficient external-memory algorithms for some geometric problems. In particular, as the ...

Generating Massive Scale-Free Networks under Resource Constraints.

Abstract: Random graphs as mathematical models of massive scale-free networks have recently become very popular. While a number of interesting properties of them have been proven, huge instances of such networks actually need to be generated for experimental evaluation and to provide artificial data sets. In this paper, we consider generation methods for random graph models based on linear preferential attachment under limited computational resources and investigate our techniques using the well-known Barabasi-Albert (BA) graph model. We present the first two I/O-efficient BA generators, MP-BA and TFP-BA, for the external-memory (EM) model and then extend MP-BA to massive parallelism based on but not limited to GPGPU. Our simple and easily generalizable sequential TFP-BA outperforms a highly tuned implementation of the sequential lineartime BB-BA algorithm by Batagelj and Brandes by several orders of magnitude once the graph size exceeds the available RAM by only 2 %. An implementation of MP-BA targeting heterogeneous systems with CPUs and GPUs is 17.6 times faster than BB-BA for instances fitting in main memory and scales well in the EM setting. Both schemes support a number of features in more general preferential attachment models, e.g., seed graphs exceeding main memory, vertices with random initial degrees, the uniform sampling of vertices, directed graphs and edges between two randomly chosen vertices. Compared with previous studies on computer clusters, MP-BA yields competitive results and already poses a viable alternative using only a single machine.

A Parallelization of Dijkstra's Shortest Path Algorithm

Abstract: The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-efficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in [0,1]. We use the G (n, d/n) model: the graph consists of n nodes and each edge is chosen with probability d/n. Our PRAM algorithm needs O(n 1/3 log n) log n) time and O (n log n+dn) work with high probability (whp). We also give extensions to external memory computation. Simulations show the applicability of our approach even on non-random graphs.

Machine learning

Abstract: Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Pregel: a system for large-scale graph processing

Abstract: Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs - in some cases billions of vertices, trillions of edges - poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distribution-related details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.

Proceedings of the National Academy of Sciences

Abstract: where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)