Faster Parallel Graph Connectivity Algorithms for GPU
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1 Vertex Connectivity 2 Edge Connectivity 3 Biconnectivity
1 Vertex Connectivity So far we've talked about connectivity for undirected graphs and weak and strong connec- tivity for directed graphs. For undirected graphs, we're going to now somewhat generalize the concept of connectedness in terms of network robustness. Essentially, given a graph, we may want to answer the question of how many vertices or edges must be removed in order to disconnect the graph; i.e., break it up into multiple components. Formally, for a connected graph G, a set of vertices S ⊆ V (G) is a separating set if subgraph G − S has more than one component or is only a single vertex. The set S is also called a vertex separator or a vertex cut. The connectivity of G, κ(G), is the minimum size of any S ⊆ V (G) such that G − S is disconnected or has a single vertex; such an S would be called a minimum separator. We say that G is k-connected if κ(G) ≥ k. 2 Edge Connectivity We have similar concepts for edges. For a connected graph G, a set of edges F ⊆ E(G) is a disconnecting set if G − F has more than one component. If G − F has two components, F is also called an edge cut. The edge-connectivity if G, κ0(G), is the minimum size of any F ⊆ E(G) such that G − F is disconnected; such an F would be called a minimum cut.A bond is a minimal non-empty edge cut; note that a bond is not necessarily a minimum cut. -
Simpler Sequential and Parallel Biconnectivity Augmentation
Simpler Sequential and Parallel Biconnectivity Augmentation Surabhi Jain and N.Sadagopan Department of Computer Science and Engineering, Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Chennai, India. fsurabhijain,[email protected] Abstract. For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum vertex separator. For a connected graph G with vertex connectivity k (k ≥ 1), the connectivity augmentation refers to a set S of edges whose augmentation to G increases its vertex connectivity by one. A minimum connectivity augmentation of G is the one in which S is minimum. In this paper, we focus our attention on connectivity augmentation of trees. Towards this end, we present a new sequential algorithm for biconnectivity augmentation in trees by simplifying the algorithm reported in [7]. The simplicity is achieved with the help of edge contraction tool. This tool helps us in getting a recursive subproblem preserving all connectivity information. Subsequently, we present a parallel algorithm to obtain a minimum connectivity augmentation set in trees. Our parallel algorithm essentially follows the overall structure of sequential algorithm. Our implementation is based on CREW PRAM model with O(∆) processors, where ∆ refers to the maximum degree of a tree. We also show that our parallel algorithm is optimal whose processor-time product is O(n) where n is the number of vertices of a tree, which is an improvement over the parallel algorithm reported in [3]. -
IAU Catalyst, June 2021
IAU Catalyst, June 2021 Information Bulletin Contents Editorial ............................................................................................................... 3 1 Executive Committee ....................................................................................... 6 2 IAU Divisions, Commissions & Working Groups .......................................... 8 3 News ................................................................................................................. 13 4 Scientific Meetings .......................................................................................... 16 5 IAU Offices ....................................................................................................... 18 6 Science Focus .................................................................................................. 24 7 IAU Publications .............................................................................................. 26 8 Cooperation with other Unions and Organisations ...................................... 28 9 IAU Timeline: Dates and Deadlines ................................................................ 31 2 IAU Catalyst, June 2021 Editorial My term as General Secretary has been most exciting, and has included notable events in the life of the Union, particularly the implementation of the IAU’s first global Strategic Plan (https:// www.iau.org/administration/about/strategic_plan/), which clearly states the IAU mission and goals for the decade 2020–2030. It also included the IAU’s centenary -
Specialising Dynamic Techniques for Implementing the Ruby Programming Language
SPECIALISING DYNAMIC TECHNIQUES FOR IMPLEMENTING THE RUBY PROGRAMMING LANGUAGE A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2015 By Chris Seaton School of Computer Science This published copy of the thesis contains a couple of minor typographical corrections from the version deposited in the University of Manchester Library. [email protected] chrisseaton.com/phd 2 Contents List of Listings7 List of Tables9 List of Figures 11 Abstract 15 Declaration 17 Copyright 19 Acknowledgements 21 1 Introduction 23 1.1 Dynamic Programming Languages.................. 23 1.2 Idiomatic Ruby............................ 25 1.3 Research Questions.......................... 27 1.4 Implementation Work......................... 27 1.5 Contributions............................. 28 1.6 Publications.............................. 29 1.7 Thesis Structure............................ 31 2 Characteristics of Dynamic Languages 35 2.1 Ruby.................................. 35 2.2 Ruby on Rails............................. 36 2.3 Case Study: Idiomatic Ruby..................... 37 2.4 Summary............................... 49 3 3 Implementation of Dynamic Languages 51 3.1 Foundational Techniques....................... 51 3.2 Applied Techniques.......................... 59 3.3 Implementations of Ruby....................... 65 3.4 Parallelism and Concurrency..................... 72 3.5 Summary............................... 73 4 Evaluation Methodology 75 4.1 Evaluation Philosophy -
Schematic Representation of Large Biconnected Graphs?
Schematic Representation of Large Biconnected Graphs? Giuseppe Di Battista, Fabrizio Frati, Maurizio Patrignani, and Marco Tais Roma Tre University, Rome, Italy fgdb,frati,patrigna,[email protected] Abstract. Suppose that a biconnected graph is given, consisting of a large component plus several other smaller components, each separated from the main component by a separation pair. We investigate the existence and the computation time of schematic representations of the structure of such a graph where the main component is drawn as a disk, the vertices that take part in separation pairs are points on the boundary of the disk, and the small components are placed outside the disk and are represented as non-intersecting lunes connecting their separation pairs. We consider several drawing conventions for such schematic representations, according to different ways to account for the size of the small components. We map the problem of testing for the existence of such representations to the one of testing for the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time algorithms. 1 Introduction Many of today's applications are based on large-scale networks, having billions of vertices and edges. This spurred an intense research activity devoted to finding methods for the visualization of very large graphs. Several recent contributions focus on algorithms that produce drawings where either the graph is only partially represented or it is schematically visualized. Examples of the first type are proxy drawings [6,12], where a graph that is too large to be fully visualized is represented by the drawing of a much smaller proxy graph that preserves the main features of the original graph. -
Balanced Vertex-Orderings of Graphs
Balanced Vertex-Orderings of Graphs Therese Biedl 1 Timothy Chan 1 School of Computer Science, University of Waterloo Waterloo, ON N2L 3G1, Canada. Yashar Ganjali 2 Department of Electrical Engineering, Stanford University Stanford, CA 94305, U.S.A. MohammadTaghi Hajiaghayi 3 Laboratory for Computer Science, Massachusetts Institute of Technology Cambridge, MA 02139, U.S.A. David R. Wood 4,∗ School of Computer Science, Carleton University Ottawa, ON K1S 5B6, Canada. Abstract In this paper we consider the problem of determining a balanced ordering of the vertices of a graph; that is, the neighbors of each vertex v are as evenly distributed to the left and right of v as possible. This problem, which has applications in graph drawing for example, is shown to be NP-hard, and remains NP-hard for bipartite simple graphs with maximum degree six. We then describe and analyze a number of methods for determining a balanced vertex-ordering, obtaining optimal orderings for directed acyclic graphs, trees, and graphs with maximum degree three. For undirected graphs, we obtain a 13/8-approximation algorithm. Finally we consider the problem of determining a balanced vertex-ordering of a bipartite graph with a fixed ordering of one bipartition. When only the imbalances of the fixed vertices count, this problem is shown to be NP-hard. On the other hand, we describe an optimal linear time algorithm when the final imbalances of all vertices count. We obtain a linear time algorithm to compute an optimal vertex-ordering of a bipartite graph with one bipartition of constant size. Key words: graph algorithm, graph drawing, vertex-ordering. -
Stefano Meschiari Education W
Stefano Meschiari education W. J. McDonald Fellow, University of Texas at Austin 2012 Doctor of Philosophy Astronomy & Astrophysics UT Austin, Department of Astronomy University of California, Santa Cruz H +1 (512) 471-3574 B [email protected] 2006 Master of Science (with highest honors) m http://stefano-meschiari.github.io Astronomy m http://www.save-point.io University of Bologna, Italy 2004 Bachelor of Science (with highest honors) research interests Astronomy • Extra-solar planet detection and dynamical modeling University of Bologna, Italy of radial velocity and transit data • N-body and hydrodynamical simulations applied to publications 17 refereed papers, 8 1st-author, h=12 proto-planetary disk evolution and planetary forma- Meschiari, S., Circumbinary Planet Formation in the Kepler- tion 16 System. II. A Toy Model for In-situ Planet Formation within • Data analysis through high-performance algorithms a Debris Belt, 2014, ApJ and citizen science Meschiari, S., Planet Formation in Circumbinary Configu- • Education and outreach through online engagement. rations: Turbulence Inhibits Planetesimal Accretion, 2012, ApJL work & research experience Meschiari, S., Circumbinary planet formation in the Kepler- 16 system. I. N-Body simulations, 2012, ApJ 2012-Present W. J. McDonald Postdoctoral Fellow Meschiari, S., et al., The Lick-Carnegie Survey: Four New University of Texas at Austin Exoplanet Candidates, 2011, ApJ Conduct research on planet formation in disturbed Meschiari, S. & Laughlin, G., Systemic: a testbed for charac- environments through numerical simulations, lead the terizing the detection of extrasolar planets. II. Full solutions development of the Systemic software for use in the data to the Transit Timing inverse problem, 2010, ApJ analysis pipeline of the Automated Planet Finder telescope Meschiari, S., Wolf, A. -
Lista Ofrecida Por Mashe De Forobeta. Visita Mi Blog Como Agradecimiento :P Y Pon E Me Gusta En Forobeta!
Lista ofrecida por mashe de forobeta. Visita mi blog como agradecimiento :P Y pon e Me Gusta en Forobeta! http://mashet.com/ Seguime en Twitter si queres tambien y avisame que sos de Forobeta y voy a evalu ar si te sigo o no.. >>@mashet NO ABUSEN Y SIGAN LOS CONSEJOS DEL THREAD! http://blog.newsarama.com/2009/04/09/supernaturalcrimefightinghasanewname anditssolomonstone/ http://htmlgiant.com/?p=7408 http://mootools.net/blog/2009/04/01/anewnameformootools/ http://freemovement.wordpress.com/2009/02/11/rlctochangename/ http://www.mattheaton.com/?p=14 http://www.webhostingsearch.com/blog/noavailabledomainnames068 http://findportablesolarpower.com/updatesandnews/worldresponsesearthhour2009 / http://www.neuescurriculum.org/nc/?p=12 http://www.ybointeractive.com/blog/2008/09/18/thewrongwaytochooseadomain name/ http://www.marcozehe.de/2008/02/29/easyariatip1usingariarequired/ http://www.universetoday.com/2009/03/16/europesclimatesatellitefailstoleave pad/ http://blogs.sjr.com/editor/index.php/2009/03/27/touchinganerveresponsesto acolumn/ http://blog.privcom.gc.ca/index.php/2008/03/18/yourcreativejuicesrequired/ http://www.taiaiake.com/27 http://www.deadmilkmen.com/2007/08/24/leaveusaloan/ http://www.techgadgets.in/household/2007/06/roboamassagingchairresponsesto yourvoice/ http://blog.swishzone.com/?p=1095 http://www.lorenzogil.com/blog/2009/01/18/mappinginheritancetoardbmswithst ormandlazrdelegates/ http://www.venganza.org/about/openletter/responses/ http://www.middleclassforum.org/?p=405 http://flavio.castelli.name/qjson_qt_json_library http://www.razorit.com/designers_central/howtochooseadomainnameforapree -
Pure Graph Algorithms
Lecture IV Page 1 “Liesez Euler, liesez Euler, c’est notre maˆıtre a´ tous” (Read Euler, read Euler, he is our master in everything) — Pierre-Simon Laplace (1749–1827) Lecture IV PURE GRAPH ALGORITHMS Graph Theory is said to have originated with Euler (1707–1783). The citizens of the city1 of K¨onigsberg asked him to resolve their favorite pastime question: is it possible to traverse all the 7 bridges joining two islands in the River Pregel and the mainland, without retracing any path? See Figure 1(a) for a schematic layout of these bridges. Euler recognized2 in this problem the essence of Leibnitz’s earlier interest in founding a new kind of mathematics called “analysis situs”. This can be interpreted as topological or combinatorial analysis in modern language. A graph correspondingto the 7 bridges and their interconnections is shown in Figure 1(b). Computational graph theory has a relatively recent history. Among the earliest papers on graph algorithms are Boruvka’s (1926) and Jarn´ık (1930) minimum spanning tree algorithm, and Dijkstra’s shortest path algorithm (1959). Tarjan [7] was one of the first to systematically study the DFS algorithm and its applications. A lucid account of basic graph theory is Bondy and Murty [3]; for algorithmic treatments, see Even [5] and Sedgewick [6]. A D B C The real bridge Credit: wikipedia (a) (b) Figure 1: The 7 Bridges of Konigsberg Graphs are useful for modeling abstract mathematical relations in computer science as well as in many other disciplines. Here are some examples of graphs: Adjacency between Countries Figure 2(a) shows a political map of 7 countries. -
A Generic Framework for the Topology-Shape-Metrics Based Layout
A Generic Framework for the Topology-Shape-Metrics Based Layout Paul Klose Master Thesis October 2012 Christian-Albrechts-Universität zu Kiel Real-Time and Embedded Systems Group Prof. Dr. Reinhard von Hanxleden Advised by: Dipl-Inf. Miro Spönemann Abstract Modeling is an important part of software engineering, but it is also used in many other areas of application. In that context the arrangement of diagram elements by hand is not efficient. Thus, layout algorithms are used to create or rearrange the diagram elements automatically in order to free users from this. However, different types of diagrams require different types of layout algorithms. Planarity and orthogonality are well-known drawing conventions for many domains such as UML class diagrams, circuit schemata or entity-relationship models. One approach to arrange such diagrams is considered by Roberto Tamassia and is called Topology-Shape-Metrics approach, which minimizes edge crossings and generates compact orthogonal grid drawings. This basic approach works with three phases: the planarization, the orthogonalization, and the compaction. The implementation of these phases are considered in this thesis in detail with respect to a generic, extensible architecture, such that every phase can be exchanged with different alternatives. This leads to a considerable amount of flexibility and expandability. Special handling of high-degree nodes has been implemented based on this architecture. Moreover, approach and implementation proposals for interactive planarization and for handling edge labels, hypergraphs and port constraints are presented. iii Eidesstattliche Erklärung Hiermit erkläre ich an Eides statt, dass ich die vorliegende Arbeit selbstständig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel verwendet habe. -
Download This Issue (Pdf)
Volume 46 Number 1 JAAVSO 2018 The Journal of the American Association of Variable Star Observers Optical Flares and Quasi-Periodic Pulsations on CR Draconis during Periastron Passage Upper panel: 2017-10-10-flare photon counts, time aligned with FFT spectrogram. Lower panel: FFT spectrogram shows time in UT seconds versus QPP periods in seconds. Flares cited by Doyle et al. (2018) are shown with (*). Also in this issue... • The Dwarf Nova SY Cancri and its Environs • KIC 8462852: Maria Mitchell Observatory Photographic Photometry 1922 to 1991 • Visual Times of Maxima for Short Period Pulsating Stars III • Recent Maxima of 86 Short Period Pulsating Stars Complete table of contents inside... The American Association of Variable Star Observers 49 Bay State Road, Cambridge, MA 02138, USA The Journal of the American Association of Variable Star Observers Editor John R. Percy Kosmas Gazeas Kristine Larsen Dunlap Institute of Astronomy University of Athens Department of Geological Sciences, and Astrophysics Athens, Greece Central Connecticut State University, and University of Toronto New Britain, Connecticut Toronto, Ontario, Canada Edward F. Guinan Villanova University Vanessa McBride Associate Editor Villanova, Pennsylvania IAU Office of Astronomy for Development; Elizabeth O. Waagen South African Astronomical Observatory; John B. Hearnshaw and University of Cape Town, South Africa Production Editor University of Canterbury Michael Saladyga Christchurch, New Zealand Ulisse Munari INAF/Astronomical Observatory Laszlo L. Kiss of Padua Editorial Board Konkoly Observatory Asiago, Italy Geoffrey C. Clayton Budapest, Hungary Louisiana State University Nikolaus Vogt Baton Rouge, Louisiana Katrien Kolenberg Universidad de Valparaiso Universities of Antwerp Valparaiso, Chile Zhibin Dai and of Leuven, Belgium Yunnan Observatories and Harvard-Smithsonian Center David B. -
Developing Interactive Web Applications For
DEVELOPING INTERACTIVE WEB APPLICATIONS FOR MANAGEMENT OF ASTRONOMY DATA By Dan Burger Thesis Submitted to the Faculty of the Graduate School of Vanderbilt University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Computer Science May, 2013 Nashville, Tennessee Approved: Professor Keivan G. Stassun Associate Professor William H. Robinson DEDICATION To Naomi, Arnold, Anat, Oded and Sarah ii ACKNOWLEDGEMENTS This year marks my seventeenth year of affiliation with Vanderbilt University: two years as a graduate student, one year as a staff member, four years as an undergraduate student, and ten years of taking piano lessons at the Blair School of Music. I am thankful that Vanderbilt has continued to support me after all these years. I am grateful for all the experiences that I have had here, the professors that have guided me and the friends that I have made along the way. Four years ago, Prof. Keivan Stassun gave me a chance to work on a project for a summer research program for undergraduates at Vanderbilt. He has supported me ever since, and I would like to thank him in particular for his kind and generous support. I would like to acknowledge the various members of the Stassun research group who have guided my research during this time and helped me to organize and revise the ideas in my thesis, specifically Dr. William Robinson, Dr. Joshua Pepper, Dr. Martin Paegert, Dr. Nathan DeLee, and Rob Siverd. I would also like to acknowledge the various users of Filtergraph and the KELT voting system who have provided valuable feedback, as well as financial support from a NASA ADAP grant and from the Vanderbilt Initiative in Data-intensive Astrophysics (VIDA).