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.

DFG Priority Programme SPP 1736: Algorithms for Big Data

Abstract: Volume, Velocity, and Variety are the three Vs commonly used to define the term big data. Simply put, those refer to the increasing amount of new data created, the increasing rate at which it is created, and the increasing number of different formats it has. At the same time, the three Vs describe challenges that require new algorithmic approaches. In order to tackle those challenges, the German Research Foundation established in 2013 the priority programme SPP 1736: Algorithms for Big Data. In this article we give a short overview on the research topics represented within this priority programme.

Algorithm Engineering für moderne Hardware

Abstract: Die Entwicklung von effizienten Algorithmen basiert auf der theoretischen Modellierung der Rechner, auf denen sie ausgefuhrt werden sollen. Noch heute werden fruhe Rechnermodelle wie die Random Access Machine (RAM) verwendet, um die Gute von Algorithmen zu analysieren und untereinander zu vergleichen. Aber sich verandernde Umstande wie der rasante Anstieg von interessanten Instanzgrosen, technologischer Fortschritt sowie neue Kostenmase stellen neue Anforderungen an die Bewertung von Algorithmen – und damit auch an ihre Enwicklung.

On Dynamic Breadth-First Search in External-Memory

Abstract: We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially $n$ nodes and O(n) edges and monotone update sequences of either $\Theta(n)$ edge insertions or $\Theta(n)$ edge deletions, we prove an amortized high-probability bound of $O(n/B^{2/3}+\sort(n)\cdot \log B)$ I/Os per update. In contrast, the currently best approach for static BFS on sparse undirected graphs requires $\Omega(n/B^{1/2}+\sort(n))$ I/Os.

Breadth first search on massive graphs

Abstract: 9th Implementation Challenge of DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, Piscataway, NJ, 22 March 2006

Energy-Ecient Fast Sorting 2011

Abstract: Authors of this report participated in the Sort Benchmark contests in 2009 and 2010. In 2009, our DEMSort program took the lead in the then-new Indy Gray category [RSSK09, RSS10], sorting 100 TB on a cluster with about 200 nodes. A tie was declared with Yahoo, whose Hadoop-based program achieved about the same result in the Daytona class, but with 17 times the hardware effort. Former results in the then-expired Indy Terabyte category were outperformed by a factor of 3–4, the same for the Indy Minute results, beating Yahoo’s new Daytona Minute result by almost a factor of 2. In 2010, our group focused on energy efficiency [BMSS10b, BMSS10a]. With specifically selected hardware, namely a machine featuring an Atom processor and four solid state disks, we improved the records in the different Indy and Gray size categories by factors of up to 5. For the 10 GB inputs, we were slightly beaten by FAWNsort [VTA10] though. However, the better result of FAWNsort is mostly due to the large 12 GiB of RAM, which fits the whole input, so this approach does not scale much further. Due to disk space restrictions, we had not been able to submit a valid result for the 1 TB Daytona Joule category. To fill in this gap, we have run this category on a standard server machine, and report the results here. In the meantime, in 2010, TritonSort [RMM10] took over the lead in the Indy Minute and Indy Gray categories, although beating DEMSort by just a few percent, which was considered a tie in the Gray case by the committee. Just as DEMSort, TritonSort exploits the given hardware very well, it uses about the same number of disks. However, the described algorithm is quite basic, and seems to work well only for uniformly distributed input, but not in general. In particular, it is unclear how the distribution step works. Sampling or something similar is not mentioned, so the splitters are probably hard-coded for the Sort Benchmark input. Worst-case inputs would probably crash the program due to bad load-balance and out-of-space problems. In contrast to that, DEMSort gives worst-case guarantees. In order to be competitive using a machine with little computational power, we had tuned our algorithms already for our 2010 JouleSort submissions. These improvements included using one file per sorted run instead of one file per block, using radix sort for the internal sorting, reading/writing many blocks at once where possible (range I/O), and fixing a bug that prevented full overlap of I/O with computation and communication. By utilizing the improved version, we hoped for just a small improvement, in order to regain the lead. However, none of the improvements has helped for Minute Sort, where there is only one pass and one sorted run, and sorting does not have to be in-place. So we had to resort to the 100 TB case, running the improved DEMSort program on the same machine as in 2009.

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)