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Deterministic sorting in nearly logarithmic time on the hypercube and related computers

Robert Cypher, C.Greg Plaxton
1993 Journal of computer and system sciences (Print)  
However, the intriguing question of existence of an O(log n) deterministic sorting algorithm for the hypercube and related computers remains open.  ...  The main result of this paper is a deterministic sorting algorithm, called Sharesort, that sorts it records in O(log n(log log n)2) time on an n-processor hypercube, shuffle-exchange, or cube-connected  ... 
doi:10.1016/0022-0000(93)90043-v fatcat:nee44zemwffz3hy34zerczv4qq

Sorting and selection on interconnection networks [chapter]

Sanguthevar Rajasekaran
1995 DIMACS Series in Discrete Mathematics and Theoretical Computer Science  
In this paper we identify techniques that have been employed in the design of sorting and selection algorithms for various interconnection networks.  ...  Interconnection Networks of interest include the mesh, the mesh with fixed and reconfigurable buses, the hypercube family, and the star graph.  ...  In [29] , Krizanc, Rajasekaran, and Shende show that on M f also, sorting can be done in time that is nearly the same as the time needed for packet routing.  ... 
doi:10.1090/dimacs/021/19 dblp:conf/dimacs/Rajasekaran94 fatcat:gw6blsftargqffge4p5nl3bgnm

Page 7456 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
Greg (1-TX-C; Austin, TX) Deterministic sorting in nearly logarithmic time on the hypercube and related computers.  ...  The main result of this paper is a deterministic sorting algorithm which works in time O(log n(log log )?) on the hypercube, shuffle- exchange and cube-connected cycles.  ... 

Sorting-Based Selection Algorithms for Hypercubic Networks

P. Berthomé, A. Ferreira, B. M. Maggs, S. Perennes, C. G. Plaxton
2000 Algorithmica  
All of the algorithms are based on the selection algorithm of Cole and Yap, as well as on various sorting algorithms for hypercubic networks.  ...  This paper presents several deterministic algorithms for selecting the kth largest record from a set of n records on any n-node hypercubic network.  ...  We are grateful to the anonymous referee for insightful remarks that helped to improve the presentation considerably.  ... 
doi:10.1007/s004539910011 fatcat:csavut7zpzad3apqkex3ze76ve

Hypercubic Sorting Networks

Tom Leighton, C. Greg Plaxton
1998 SIAM journal on computing (Print)  
possible input permutations, (ii) an O(lg n)-depth hypercubic comparator network that sorts the vast majority of permutations, (iii) a hypercubic sorting network with nearly logarithmic depth, (iv) an  ...  previously known algorithm), and (v) a randomized algorithm for sorting n O(m)-bit records on an (n lg n)-node omega network in O(m + lg n) bit steps.  ...  Acknowledgments Thanks to Don Coppersmith, Ming Kao, Sheralyn Listgarten, Yuan Ma, Bruce Maggs, and Torsten Suel for valuable discussions.  ... 
doi:10.1137/s0097539794268406 fatcat:qtz5of4v5na7de5xd3jz6tc6oq

Deterministic approximation of marginal probabilities in Bayes nets

E. Santos, S.E. Shimony
1998 IEEE transactions on systems, man and cybernetics. Part A. Systems and humans  
Computation of marginal probabilities in Bayes nets is central to numerous reasoning and automatic decision making systems.  ...  In the best-first search algorithm, other schemes are necessary, but experimental results suggest that using inclusion-exclusion (potentially exponential-time in the worst case) in the overlap cases is  ...  Related Work The work on term computation [13] and related papers are extremely relevant to this paper.  ... 
doi:10.1109/3468.686701 fatcat:di4weauyzrdrjpcsasyjxwy6hy

Thermal Response Variability of Random Polycrystalline Microstructures

Bin Wen, Zheng Li, Nicholas Zabaras
2011 Communications in Computational Physics  
We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation  ...  This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture  ...  Zabaras) acknowledges support from the Computational Mathematics program of AFOSR (grant F49620-00-1-0373), the DOE Office of Science ASCR (award DE-SC0004910), the Materials Design and Surface Engineering  ... 
doi:10.4208/cicp.200510.061210a fatcat:6sd2huhjtrel3jneqef3m757xq

A complexity theory of efficient parallel algorithms

Clyde P. Kruskal, Larry Rudolph, Marc Snir
1990 Theoretical Computer Science  
The dominant time is the sorting in steps (2) and (6), which by Lemma 4.16 is o( (;+bP) ,Z;,',).  ...  Rudnlph, M Snir Lemma 4.16 (ICruskal et al. [52], Reif [66], Wagner and Han [80]). A p processor EREW PRAM can sort n integers in the mnge 0,. _. , R -I in rime Proof of T&orem 4.8.  ...  l Gasarch, Kathy I-Gibers, Prabhakar Raghavan, and Eli Upfal. We thank Martin Dietzfelbinger for informing us of his improvement to Lemma 4.19.  ... 
doi:10.1016/0304-3975(90)90192-k fatcat:txltfl7ymzekzihnn5veh2zkta

Polyvalent Parallelizations for Hierarchical Block Matching Motion Estimation

Charalampos G. Konstantopoulos, Andreas I. Svolos, Christos Kaklamanis
2000 Journal of Computing and Information Technology  
realization of the HBMME algorithm on a hypercube-based multiprocessor.  ...  In this paper, we design an efficient hierarchical block matching motion estimation (HBMME) algorithm on a hypercube multiprocessor.  ...  Acknowledgements This work is supported in part by the General Secretariat of Research and Technology of Greece under Project ΠENE∆ 95 E∆ 1623.  ... 
doi:10.2498/cit.2000.01.05 fatcat:tkrl2di4orcx5mtiolokcqieci

The Queue-Read Queue-Write PRAM Model: Accounting for Contention in Parallel Algorithms

Phillip B. Gibbons, Yossi Matias, Vijaya Ramachandran
1998 SIAM journal on computing (Print)  
Furthermore, we present a work-preserving emulation of the qrqw pram with only logarithmic slowdown on Valiant's bsp model, and hence on hypercube-type noncombining networks, even when latency, synchronization  ...  Finally, the paper presents several lower bound results for this model, including lower bounds on the time required for broadcasting and for leader election.  ...  Richard Cole, Albert Greenberg, Maurice Herlihy, Honghua Yang, and the anonymous referees provided useful comments on this work.  ... 
doi:10.1137/s009753979427491 fatcat:bwua22baujghvesgxzawx5ky2q

All-Pairs Shortest Paths in Geometric Intersection Graphs

Timothy M. Chan, Dimitrios Skrepetos
2018 Journal of Computational Geometry  
$\OO{n^{7/3} \log^{1/3} n}$ time, $d$-dimensional axis-aligned unit hypercubes in $\OO{n^2 \log\log n}$ time for $d=3$ and $\OO{n^2 \log^{d-3} n}$ time for $d\geq4$, and $d$-dimensional axis-aligned boxes  ...  $\newcommand{\OO}[1]{O\left(#1\right)}$We present a simple and general algorithm for the all-pairs shortest paths (APSP) problem in unweighted geometric intersection graphs.  ...  In our case, the latter has already been done, and to obtain the former we employ counting sort in O (|R m | + s) time.  ... 
doi:10.20382/jocg.v10i1a2 dblp:journals/jocg/ChanS19 fatcat:7n4nsty24fcrdnjrpko43piuke

Using Orthogonal Arrays in the Sensitivity Analysis of Computer Models

Max D. Morris, Leslie M. Moore, Michael D. McKay
2008 Technometrics  
Two examples are given demonstrating the sampling plan, behavior of the estimates and standard errors, and comparative results based on other approaches.  ...  We consider a class of input sampling plans called permuted column sampling plans, that are popular in sensitivity analysis of computer models.  ...  Morris was partially supported through the Visiting Faculty Program of Los Alamos National Laboratory, and partially supported by NSF grant DMS #0502347 EMSW21-RTG awarded to the Department of Statistics  ... 
doi:10.1198/004017008000000208 fatcat:aeldbugrqncc3kph3z56pkco64

An introduction to randomized algorithms

Richard M. Karp
1991 Discrete Applied Mathematics  
The examples are drawn from many areas, including number theory, algebra, graph theory, pattern matching, selection, sorting, searching, computational geometry, combinatorial enumeration, and parallel  ...  and distributed computation.  ...  In this case, the insertion and access times are linear in n, rather than logarithmic.  ... 
doi:10.1016/0166-218x(91)90086-c fatcat:d3pgh36rvvhphcxov4p5yhvvhu

Bulk Synchronous Parallel Algorithms for the External Memory Model

Dehne, Dittrich, Hutchinson, Maheshwari
2002 Theory of Computing Systems  
It optimizes blockwise data access and parallel disk I/O and, at the same time, utilizes multiple processors connected via a communication network or shared memory.  ...  Blockwise access to data is a central theme in the design of efficient external memory (EM) algorithms. A second important issue, when more than one disk is present, is fully parallel disk I/O.  ...  The logarithmic term in the I/O complexity of sorting is bounded by a constant c if (M/B) c ≥ N /B, where M = N /v.  ... 
doi:10.1007/s00224-002-1066-2 fatcat:onmzny3fhjdzjjongxlf2sucma

Fully Scalable Fault-Tolerant Simulations for BSP and CGM

Sung-Ryul Kim, Kunsoo Park
2000 Journal of Parallel and Distributed Computing  
The faults are deterministic (i.e., worst-case distributions of faults are considered) and static (i.e., they do not change in the course of computation).  ...  Ç´ÐÓ Ôµ) slowdown per communication round, provided that a deterministic preprocessing is done that requires Ç´´ÐÓ Ôµ ¾ µ communication rounds and linear (in ) computation per processor in each communication  ...  One is a deterministic technique and the other is a randomized one.  ... 
doi:10.1006/jpdc.2000.1659 fatcat:2qjyvmcgxba5rooaslwywg56ue
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