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

2009
*
Lecture Notes in Computer Science
*

Here we further improve

doi:10.1007/978-3-642-03367-4_23
fatcat:trxhfbcgrvd3tj3mkqtmp45piq
*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. ...##
###
On reconfiguration of disks in the plane and related problems

2013
*
Computational geometry
*

Here we further improve

doi:10.1016/j.comgeo.2012.06.001
fatcat:ugxo3w3nq5gy3iodjbko5wiaja
*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. ...##
###
Layered models for closed 3-manifolds
[article]

2010
*
arXiv
*
pre-print

We define a combinatorial structure

arXiv:1011.6343v1
fatcat:kcplzacvzzctvn5hib2cdt3y3m
*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*. ...##
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On synchronisation in fault-tolerant data and compute intensive programs over a network of workstations
[chapter]

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. ...

##
###
Dynamic query scheduling in parallel data warehouses

2003
*
Concurrency and Computation
*

Data warehouse queries pose challenging performance problems that often necessitate

doi:10.1002/cpe.786
fatcat:tfnsvessw5fjzelxvfgr5zd46m
*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*. ...##
###
Dynamic Query Scheduling in Parallel Data Warehouses
[chapter]

2002
*
Lecture Notes in Computer Science
*

Data warehouse queries pose challenging performance problems that often necessitate

doi:10.1007/3-540-45706-2_43
fatcat:vijtjlvzejbbrbmijn6sappheq
*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*. ...##
###
Greed sort: optimal deterministic sorting on parallel disks

1995
*
Journal of the ACM
*

Our measure

doi:10.1145/210332.210343
fatcat:yfsc4fhmcvdqdlbzkx7jvrfm2i
*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. ...##
###
Self-replicating 3-manifolds
[article]

2021
*
arXiv
*
pre-print

In this paper we explore

arXiv:2107.04528v1
fatcat:pbynq5vpcre3jjc5einmyirfmq
*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 ). ...##
###
Distribution sort with randomized cycling

2006
*
Journal of the ACM
*

Based upon ideas in RCD we propose general techniques that transparently simulate algorithms developed for

doi:10.1145/1162349.1162352
fatcat:ksiyk7uuwbeehjannt7s3mapim
*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. ...##
###
A template for developing next generation parallel Delaunay refinement methods

2010
*
Finite elements in analysis and design
*

In

doi:10.1016/j.finel.2009.06.014
fatcat:yoev7a3fqbbgxktvvbvz3hpxt4
*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. ...##
###
Balanced Line Separators of Unit Disk Graphs
[chapter]

2017
*
Lecture Notes in Computer Science
*

We prove a geometric version

doi:10.1007/978-3-319-62127-2_21
fatcat:cwevshj445eb3emmmlrwv326lq
*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. ...##
###
Performance analysis of a pull-based parallel video server

2000
*
IEEE Transactions on Parallel and Distributed Systems
*

This paper analyzes

doi:10.1109/71.895790
fatcat:4kk4fmwjs5echcebv4ibhcfeyi
*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 ...##
###
Algorithms for parallel memory, I: Two-level memories

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 ...

##
###
Exponential separation in 4–manifolds

2000
*
Geometry and Topology
*

We use a new geometric construction, grope splitting, to give a sharp

doi:10.2140/gt.2000.4.397
fatcat:etfi4ref6zg4jb2o2hhppdv5pa
*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. ...##
###
What are the shapes of embedded minimal surfaces and why?
[article]

2005
*
arXiv
*
pre-print

Case

arXiv:math/0511740v1
fatcat:3ms335sswjfthajy43o6xhxogi
*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*. ...
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