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On Reconfiguration of Disks in the Plane and Related Problems [chapter]

Adrian Dumitrescu, Minghui Jiang
2009 Lecture Notes in Computer Science  
Here we further improve the lower bound to ⌊5n/3⌋ − 1, and thereby give a partial answer to one of their open problems.  ...  We obtain various combinatorial and computational results for these two models: (I) For systems of n congruent unlabeled disks in the translation model, Abellanas et al. showed that 2n − 1 moves always  ...  Alternatively, the configuration can be viewed as consisting of m groups of three disks each, plus two disks, one at the higher and one at the lower end of the chain along the circle of radius r.  ... 
doi:10.1007/978-3-642-03367-4_23 fatcat:trxhfbcgrvd3tj3mkqtmp45piq

On reconfiguration of disks in the plane and related problems

Adrian Dumitrescu, Minghui Jiang
2013 Computational geometry  
Here we further improve the lower bound to ⌊5n/3⌋ − 1, and thereby give a partial answer to one of their open problems.  ...  We obtain various combinatorial and computational results for these two models: (I) For systems of n congruent unlabeled disks in the translation model, Abellanas et al. showed that 2n − 1 moves always  ...  Alternatively, the configuration can be viewed as consisting of m groups of three disks each, plus two disks, one at the higher and one at the lower end of the chain along the circle of radius r.  ... 
doi:10.1016/j.comgeo.2012.06.001 fatcat:ugxo3w3nq5gy3iodjbko5wiaja

Layered models for closed 3-manifolds [article]

Jesse Johnson
2010 arXiv   pre-print
We define a combinatorial structure on 3-manifolds that combines the model manifolds constructed in Minsky's proof of the ending lamination conjecture with the layered triangulations defined by Jaco and  ...  Moreover, if one takes two parallel copies of a disk bounded by ℓ and attaches them by a band in the complement of the annulus between the boundaries of two disks, the resulting disk has boundary parallel  ...  The pair of pants F has either one or two boundary components in the models for the smaller compression bodies, depending on whether D is separating or non-separating.  ... 
arXiv:1011.6343v1 fatcat:kcplzacvzzctvn5hib2cdt3y3m

On synchronisation in fault-tolerant data and compute intensive programs over a network of workstations [chapter]

J. Smith
1997 Lecture Notes in Computer Science  
The work summarised here investigates performance of structuring approaches applicable where this ideal is not possible, partly through analysis and partly through measurements of a realistic fault-tolerant  ...  An application structured as a fault-tolerant bag of tasks adapts easily to changing resources. To be represented by a single bag of tasks, a computation must decompose into purely independent tasks.  ...  Acknowledgements The support of all the Arjuna team is gratefully acknowledged, and in particular collaboration with S.  ... 
doi:10.1007/bfb0002847 fatcat:vtqnjbs4f5br7a7yugj3dn26ou

Dynamic query scheduling in parallel data warehouses

Holger Märtens, Erhard Rahm, Thomas Stöhr
2003 Concurrency and Computation  
Data warehouse queries pose challenging performance problems that often necessitate the use of parallel database systems (PDBS).  ...  In this study, we propose a scheduling strategy that simultaneously considers both processors and disks while utilizing the load balancing potential of a Shared Disk architecture.  ...  We model the disk load characteristics of each subquery in the shape of a load vector ➀ containing the expected number of pages referenced on each disk.  ... 
doi:10.1002/cpe.786 fatcat:tfnsvessw5fjzelxvfgr5zd46m

Dynamic Query Scheduling in Parallel Data Warehouses [chapter]

Holger Märtens, Erhard Rahm, Thomas Stöhr
2002 Lecture Notes in Computer Science  
Data warehouse queries pose challenging performance problems that often necessitate the use of parallel database systems (PDBS).  ...  In this study, we propose a scheduling strategy that simultaneously considers both processors and disks while utilizing the load balancing potential of a Shared Disk architecture.  ...  We model the disk load characteristics of each subquery in the shape of a load vector ➀ containing the expected number of pages referenced on each disk.  ... 
doi:10.1007/3-540-45706-2_43 fatcat:vijtjlvzejbbrbmijn6sappheq

Greed sort: optimal deterministic sorting on parallel disks

Mark H. Nodine, Jeffrey Scott Vitter
1995 Journal of the ACM  
Our measure of performance is the number of parallel input/output (1/0) operations, in which each of the D disks can simultaneously transfer a block of B contiguous records.  ...  We present an algorithm for sorting efficiently with parallel two-level memories.  ...  Greed Sort The parameters for our two-level memory model (or parallel disk 1/0 model) in Figure where M < IV, and 1 s DB < [(M -MP)/21, for fixed~< 1.  ... 
doi:10.1145/210332.210343 fatcat:yfsc4fhmcvdqdlbzkx7jvrfm2i

Self-replicating 3-manifolds [article]

Ryan Blair, Ricky Lee
2021 arXiv   pre-print
In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category.  ...  Let E 1 and E 2 be the two disks in S bounded by ∂D. The disk D cuts B into two 3-balls B 1 and B 2 such that ∂B 1 = E 1 ∪ D and ∂B 2 = E 2 ∪D.  ...  At least one of these two 2-spheres also separates M 1 from M 2 , contradicting the minimality of S ∩f (N ).  ... 
arXiv:2107.04528v1 fatcat:pbynq5vpcre3jjc5einmyirfmq

Distribution sort with randomized cycling

Jeffrey Scott Vitter, David Alexander Hutchinson
2006 Journal of the ACM  
Based upon ideas in RCD we propose general techniques that transparently simulate algorithms developed for the unrealistic multihead disk model so that they can be run on the realistic parallel disk model  ...  Parallel independent disks can enhance the performance of external memory (EM) algorithms, but the programming task is often di cult.  ...  We thank Rakesh Barve and Peter Sanders for interesting discussions about the SRD and RSD algorithms.  ... 
doi:10.1145/1162349.1162352 fatcat:ksiyk7uuwbeehjannt7s3mapim

A template for developing next generation parallel Delaunay refinement methods

Andrey N. Chernikov, Nikos P. Chrisochoides
2010 Finite elements in analysis and design  
In the area of parallel Delaunay mesh refinement, we develop a new theoretical framework for the construction of graded meshes on parallel architectures, i.e., for parallel mesh generation with element  ...  Both types of selection disks are inside the circumdisk of a poor quality triangle, with the Type I disk always inside the Type II disk.  ...  The size of the Type I selection disks, and, hence, the flexibility in choosing Steiner points depends on the initial model and can vary significantly.  ... 
doi:10.1016/j.finel.2009.06.014 fatcat:yoev7a3fqbbgxktvvbvz3hpxt4

Balanced Line Separators of Unit Disk Graphs [chapter]

Paz Carmi, Man Kwun Chiu, Matthew J. Katz, Matias Korman, Yoshio Okamoto, André van Renssen, Marcel Roeloffzen, Taichi Shiitada, Shakhar Smorodinsky
2017 Lecture Notes in Computer Science  
We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of n unit disks in the plane there exists a line such that intersects at most O( (m + n) log  ...  We give an almost tight lower bound (up to sublogarithmic factors) for our approach, and also show that no line-separator of sublinear size in n exists when we look at disks of arbitrary radii, even when  ...  The authors thank Michael Hoffmann and Eli Fox-Epstein for motivating discussion on the topic.  ... 
doi:10.1007/978-3-319-62127-2_21 fatcat:cwevshj445eb3emmmlrwv326lq

Performance analysis of a pull-based parallel video server

J.Y.B. Lee, P.C. Wong
2000 IEEE Transactions on Parallel and Distributed Systems  
This paper analyzes the performance of the architecture by deriving bounds for server service delay, client buffer requirement, prefetch delay, and scheduling delay.  ...  Second, a client-pull service model is employed to eliminate the need for interserver synchronization.  ...  ACKNOWLEDGMENTS This research was funded in part by a research grant (CUHK6095/99E) from the HKSAR Research Grants Council and in part by the Area of Excellence in ITÐa research grant from the HKSAR University  ... 
doi:10.1109/71.895790 fatcat:4kk4fmwjs5echcebv4ibhcfeyi

Algorithms for parallel memory, I: Two-level memories

J. S. Vitter, E. A. M. Shriver
1994 Algorithmica  
The model pertains to a large-scale uniprocessor system or parallel multiprocessor system with P disks.  ...  Our two-level memory model is new and gives a realistic treatment o f p arallel block transfer, in which during a single I O each of the P secondary storage devices can simultaneously transfer a contiguous  ...  In the next section we de ne a realistic two-level memory model with parallel block transfer, which consists of an internal memory capable of storing M records and P disks, each disk capable of simultaneously  ... 
doi:10.1007/bf01185207 fatcat:linktjnicze2zm2zbn7doefbjy

Exponential separation in 4–manifolds

Vyacheslav S Krushkal
2000 Geometry and Topology  
We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4-manifolds.  ...  We also describe applications of this technique in link-homotopy theory, and to the problem of locating pi_1-null surfaces in 4-manifolds.  ...  Acknowledgements Research was supported by the Institute for Advanced Study (NSF grant DMS 97-29992) and by Harvard University.  ... 
doi:10.2140/gt.2000.4.397 fatcat:etfi4ref6zg4jb2o2hhppdv5pa

What are the shapes of embedded minimal surfaces and why? [article]

Tobias H. Colding, William P. Minicozzi II
2005 arXiv   pre-print
Case one is where the surface is a disk, in case two the surface is a planar domain (genus zero), and the third case is that of finite (non-zero) genus.  ...  The complete understanding of the disk case is applied in both cases two and three.  ...  One can easily see that the only simply connected surfaces are the disk and the sphere. Disks There are two local models for embedded minimal disks.  ... 
arXiv:math/0511740v1 fatcat:3ms335sswjfthajy43o6xhxogi
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