Sample sort on meshes

This paper provides an overview of lower and upper bounds for mesh-connected processor networks. Most attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Grammatikakis, Hsu and Kraetzl on multicomputer routing, submitted to JPDC

Aspects of practical implementations of PRAM algorithms

The PRAM is a shared memory model of parallel computation which abstracts away from inessential engineering details. It provides a very simple architecture independent model and provides a good programming environment. Theoreticians of the computer science community have proved that it is possible to emulate the theoretical PRAM model using current technology. Solutions have been found for effectively interconnecting processing elements, for routing data on these networks and for distributing the data among memory modules without hotspots. This thesis reviews this emulation and the possibilities it provides for large scale general purpose parallel computation. The emulation employs a bridging model which acts as an interface between the actual hardware and the PRAM model. We review the evidence that such a scheme crn achieve scalable parallel performance and portable parallel software and that PRAM algorithms can be optimally implemented on such practical models. In the course of this review we presented the following new results: 1. Concerning parallel approximation algorithms, we describe an NC algorithm for finding an approximation to a minimum weight perfect matching in a complete weighted graph. The algorithm is conceptually very simple and it is also the first NC-approximation algorithm for the task with a sub-linear performance ratio. 2. Concerning graph embedding, we describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the de Bruijn and shuffle-exchange networks and the 2-dimcnsional mesh. In the embeddings the maximum distance from a leaf to the root of the tree is asymptotically optimally short. The embeddings facilitate efficient implementation of many PRAM algorithms on networks employing these graphs as interconnection networks. 3. Concerning bulk synchronous algorithmics, we describe scalable transportable algorithms for the following three commonly required types of computation; balanced tree computations. Fast Fourier Transforms and matrix multiplications

Randomized priority queues for fast parallel access

Applications like parallel search or discrete event simulation often assign priority or importance to pieces of work. An effective way to exploit this for parallelization is to use a priority queue data structure for scheduling the work; but a bottleneck free implementation of parallel priority queue access by many processors is required to make this approach scalable. We present simple and portable randomized algorithms for parallel priority queues on distributed memory machines with fully distributed storage. Accessing O(n) out of m elements on an n-processor network with diameter d requires amortized time O(d + log m/n) with high probability for many network types. On logarithmic diameter networks, the algorithms are as fast as the best previously known EREW-PRAM methods. Implementations demonstrate that the approach is already useful for medium scale parallelism

Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Tensor lattice field theory with applications to the renormalization group and quantum computing

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group program. Tensor reformulations are naturally discrete and provide manageable transfer matrices. Combining truncations with the time continuum limit, we derive Hamiltonians suitable to perform quantum simulation experiments, for instance using cold atoms, or to be programmed on existing quantum computers. We review recent progress concerning the tensor field theory treatment of non-compact scalar models, supersymmetric models, economical four-dimensional algorithms, noise-robust enforcement of Gauss's law, symmetry preserving truncations and topological considerations. We discuss connections with other tensor network approaches.Comment: Review article, 71 pages, 47 figures, connections to other tensor network approaches and references adde

Report / Institute für Physik

The 2014 Report of the Physics Institutes of the Universität Leipzig presents a hopefully interesting overview of our research activities in the past year. It is also testimony of our scientific interaction with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within the work groups. The open full professorship in the Institute for Experimental Physics I has been filled with an outstanding candidate. We could attract Prof. Ralf Seidel from the University of Münster. He is an expert in molecular biophysics that complements the existing strength in cellular biophysics. Prof. Hollands could fill all positions of his ERC Starting Grant, so that the work on the project \"Quantum Fields and Curvature – Novel Constructive Approach via Operator Product Expansion\" is now running at full pace. Within the Horizon 2020 project LOMID \"Large Cost-effective OLED Microdisplays and their Applications\" (2015-2017) with eight European partners including industry the semiconductor physics group contributes with transparent oxide devices. A joint laboratory for single ion implantation was established between the Leibniz-Institute for Surface Modification (IOM) and the university under the guidance of Profs. Rauschenbach and Meijer. The EU IRSES Network DIONICOS \"Dynamics of and in Complex Systems\", a consortium of 6 European and 12 non-European partners, including sites in England, France and Germany as well as in Russia, Ukraine, India, the United States and Venezuela, started in February 2014. In the next four years the Leipzig node headed by Prof. Janke will profit from the numerous international contacts this network provides. With a joint project, Prof. Kroy and Prof. Cichos participate in the newly established priority research programme SPP 1726 \"Microswimmers\", which started with a kick-off workshop in October 2014. In 2014 the International Graduate College \"Statistical Physics of Complex Systems\" run by the computational physics group has commenced its third 3-years granting period funded by Deutsch-Französische Hochschule (DFH-UFA). Besides the main partner Université de Lorraine in Nancy, France, now also Coventry University, UK, and the Institute for Condensed Matter Physis of the National Academy of Sciences of Ukraine in Lviv, Ukraine, participate as associated partners. During the last week of September the TCO2014 conference \"Transparent Conductive Oxides – Fundamentals and Applications\" took place in honor of the 100th anniversary of the death of Prof. Dr. KarlW. Bädeker. In 1907 Karl Bädeker had discovered transparent conductive materials and oxides in Leipzig. About a hundred participants joined for many invited talks from international experts, intense discussion and new cooperations. At the end of November the by now traditional 15th nternational Workshop on Recent Developments in Computational Physics \"CompPhys14\" organized by Prof. Janke took place in Leipzig. Around 60 scientists from over 10 different countries exchanged ideas and discussed recent progress in several fields of computational physics. Work has successfully continued in the Centers of Excellence (Sonderforschungsbereiche) SFB 762 \"Functionality ofOxide Interfaces\" and SFB TRR 102 \"Polymers under Multiple Constraints: Restricted and Controlled Molecular Order and Mobility\" (just renewed for 2015-2019). Our activities and success are only possible with the generous support fromvarious funding agencies for which we are very grateful and which is individually acknowledged in the brief reports