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.

External-memory breadth-first search with sublinear I/O

Abstract: Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires Θ(n + n+m/D.B . log M/B n+m/B) I/Os on a graph with n nodes and m edges and a machine with main-memory of size M, D parallel disks, and block size B. We present a new approach which requires only O( + √n.(n+m/D.B + n+m/D.B . log M/B n+m/B)I/Os. Hence, for m = O(n) and all realistic values of log m/B n+m/B, it improves upon the I/O-performance of the best previous algorithm by a factor Ω(√D.B). Our approach is fairly simple and we conjecture it to be practical. We also give improved algorithms for undirected single-source shortest-paths with small integer edge weights and for semi-external BFS on directed Eulerian graphs.

External-Memory Breadth-First Search with Sublinear I/O

Abstract: Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires ?(n + n+m/D?B ? logM/B n+m/B) I/Os on a graph with n nodes and m edges and a machine with main-memory of size M, D parallel disks, and block size B. We present a new approach which requires only O(?n?(n+m)/D?B + n+m/D?B ? logM/B n+m/B)I/Os. Hence, for m = O(n) and all realistic values of logM/B n+m/B, it improves upon the I/O-performance of the best previous algorithm by a factor ?(?D ? B). Our approach is fairly simple and we conjecture it to be practical. We also give improved algorithms for undirected single-source shortest-paths with small integer edge weights and for semi-external BFS on directed Eulerian graphs.

Characterizing the performance of flash memory storage devices and its impact on algorithm design

Abstract: Initially used in digital audio players, digital cameras, mobile phones, and USB memory sticks, flash memory may become the dominant form of end-user storage in mobile computing, either completely replacing the magnetic hard disks or being an additional secondary storage. We study the design of algorithms and data structures that can exploit the flash memory devices better. For this, we characterize the performance of NAND flash based storage devices, including many solid state disks. We show that these devices have better random read performance than hard disks, but much worse random write performance. We also analyze the effect of misalignments, aging and past I/O patterns etc. on the performance obtained on these devices. We show that despite the similarities between flash memory and RAM (fast random reads) and between flash disk and hard disk (both are block based devices), the algorithms designed in the RAM model or the external memory model do not realize the full potential of the flash memory devices. We later give some broad guidelines for designing algorithms which can exploit the comparative advantages of both a flash memory device and a hard disk, when used together.

Delta-Stepping: A Parallel Single Source Shortest Path Algorithm

Abstract: In spite of intensive research, little progress has been made towards fast and work-efficient parallel algorithms for the single source shortest path problem. Our Δ-stepping algorithm, a generalization of Dial's algorithm and the Bellman-Ford algorithm, improves this situation at least in the following "average-case" sense: For random directed graphs with edge probability d/n and uniformly distributed edge weights a PRAM version works in expected time O(log3 n/ log log n) using linear work. The algorithm also allows for efficient adaptation to distributed memory machines. Implementations show that our approach works on real machines. As a side effect, we get a simple linear time sequential algorithm for a large class of not necessarily random directed graphs with random edge weights.

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)