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.

Parallel and I/O-efficient Randomisation of Massive Networks using Global Curveball Trades

Abstract: Graph randomisation is a crucial task in the analysis and synthesis of networks. It is typically implemented as an edge switching process (ESMC) repeatedly swapping the nodes of random edge pairs while maintaining the degrees involved [Mihail and Zegura, 2003]. Curveball is a novel approach that instead considers the whole neighbourhoods of randomly drawn node pairs. Its Markov chain converges to a uniform distribution, and experiments suggest that it requires less steps than the established ESMC [Carstens et al., 2016]. Since trades however are more expensive, we study Curveball's practical runtime by introducing the first efficient Curveball algorithms: the I/O-efficient EM-CB for simple undirected graphs and its internal memory pendant IM-CB. Further, we investigate global trades [Carstens et al., 2016] processing every node in a single super step, and show that undirected global trades converge to a uniform distribution and perform superior in practice. We then discuss EM-GCB and EM-PGCB for global trades and give experimental evidence that EM-PGCB achieves the quality of the state-of-the-art ESMC algorithm EM-ES [M. Hamann et al., 2017] nearly one order of magnitude faster.

Mechanisms with Monitoring for truthful RAM allocation

Abstract: Novel algorithmic ideas for big data have not been accompanied by advances in the way central memory is allocated to concurrently running programs. Commonly, RAM is poorly managed since the programs' trade offs between speed of execution and RAM consumption are ignored. This trade off is, however, well known to the programmers. We adopt mechanism design tools to truthfully elicit this multidimensional information with the aim of designing more clever RAM allocation algorithms. We introduce a novel paradigm wherein programs are bound to overbidding declarations of their running times. We show the limitations of this paradigm in the absence of transfers and prove how to leverage waiting times, as a currency, to obtain optimal money burning mechanisms for the makespan.

Matrix transpose on meshes: theory and practice

Abstract: Matrix transpose is a fundamental communication operation which is not dealt with optimally by general purpose routing schemes. For two dimensional meshes, the first optimal routing schedule is given. The strategy is simple enough to be implemented, but details of the available hardware are not favorable. However, alternative algorithms, designed along the same lines, give an improvement on the Intel Paragon.

Single-Source Shortest-Paths on Arbitrary Directed Graphs in Linear Average-Case Time

Abstract: The quest for a linear-time single-source shortest-path (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic. While Thorup recently found an O(n + m) time RAM algorithm for undirected graphs with n nodes, m edges and integer edge weights in {0,…,2w - 1} where w denotes the word length, the currently best time bound for directed sparse graphs on a RAM is O(n + m · log log n).In the present paper we study the average-case complexity of SSSP. We give a simple algorithm for arbitrary directed graphs with random edge weights uniformly distributed in [0, 1] and show that it needs linear time O(n + m) with high probability.

I/O-efficient approximation of graph diameters by parallel cluster growing — A first experimental study

Abstract: A fundamental step in the analysis of a massive graph is to compute its diameter. In the RAM model, the diameter of a connected undirected unweighted graph can be efficiently 2-approximated using a Breadth-First Search (BFS) traversal from an arbitrary node. However, if the graph is stored on disk, even an external memory BFS traversal is prohibitive, owing to the large number of I/Os it incurs. Meyer [1] proposed a parametrized algorithm to compute an approximation of graph diameter with fewer I/Os than that required for exact BFS traversal of the graph. The approach is based on growing clusters around randomly chosen vertices ‘in parallel’ until their fringes meet. We present an implementation of this algorithm and compare it with some simple heuristics and external-memory BFS in order to determine the trade-off between the approximation ratio and running-time achievable in practice. Our experiments show that with carefully chosen parameters, the new approach is indeed capable to produce surprisingly good diameter approximations in shorter time. We also confirm experimentally, that there are graph-classes where the parametrized approach runs into bad approximation ratios just as the theoretical analysis in [1] suggests.

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)