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.

A simple improved distributed algorithm for minimum CDS in unit disk graphs

Abstract: Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via back-bone nodes. One common way of constructing such a backbone is based on the construction of a minimum connected dominating set (CDS). In this paper we present a very simple distributed algorithm for computing a small CDS. Our algorithm has an approximation factor of at most 6.91, improving upon the previous best known approximation factor of 8 due to Wan et al. [INFOCOM'02], The improvement relies on a refined analysis of the relationship between the size of a maximal independent set and a minimum CDS in a unit disk graph. This subresult also implies improved approximation factors for many existing algorithm.

Heaps Are Better than Buckets: Parallel Shortest Paths on Unbalanced Graphs

Abstract: We propose a new parallel algorithm for the single-source shortest-path problem (SSSP). Its heap data structure is particularly advantageous on graphs with a moderate number of high degree nodes. On arbitrary directed graphs with n nodes, m edges and independent random edge weights uniformly distributed in the range [0, 1] and maximum shortest path weight L the PRAM version of our algorithm runs in O(log2 nċmini{2iċLċlog n+|Vi|}) average-case time using O(nċlog n+m) operations where |Vi| is the number of graph vertices with degree at least 2i. For power-law graph models of the Internet or call graphs this results in the first work-efficient o(n1/4) average-case time algorithm.

Towards practical permutation routing on meshes

Abstract: We consider the permutation routing problem on two-dimensional n/spl times/n meshes. To be practical, a routing algorithm is required to ensure very small queue sizes Q, and very low running time T, not only asymptotically but particularly also for the practically important n up to 1000. With a technique inspired by a scheme of Kaklamanis/Krizanc/Rao, we obtain a near-optimal result: T=2/spl middot/n+/spl Oscr/(1) with Q=2. Although Q is very attractive now, the lower order terms in T make this algorithm highly impractical. Therefore we present simple schemes which are asymptotically slower, but have T/spl sime/3/spl middot/n for all n and Q between 2 and 8. >

Theory and Practice of Time-Space Trade-Offs in Memory Limited Search

Abstract: Having to cope with memory limitations is an ubiquitous issue in heuristic search. We present theoretical and practical results on new variants for exploring state-space with respect to memory limitations.We establish O(log n) minimum-space algorithms that omit both the open and the closed list to determine the shortest path between every two nodes and study the gap in between full memorization in a hash table and the information-theoretic lower bound. The proposed structure of suffix-lists elaborates on a concise binary representation of states by applying bit-state hashing techniques. Significantly more states can be stored while searching and inserting n items into suffix lists is still available in O(n log n) time. Bit-state hashing leads to the new paradigm of partial iterative-deepening heuristic search, in which full exploration is sacrificed for a better detection of duplicates in large search depth. We give first promising results in the application area of communication protocols.

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.

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)