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Optimal Routing of Parentheses on the Hypercube

E.W. Mayr, R. Werchner
1995 Journal of Parallel and Distributed Computing  
We consider a new class of routing requests or partial permutations for which we give optimal on-line routing algorithms on the hypercube and shu e-exchange network.  ...  For well-formed words of parentheses our algorithm establishes communication between all matching pairs in logarithmic time.  ...  Hence, these routings can be performed in logarithmic time on a hypercube, and a variety of related problems can be solved e ciently or even optimally.  ... 
doi:10.1006/jpdc.1995.1058 fatcat:bxa4sz6s3ncl7hrzwopivslkfq

Optimal Tree Contraction and Term Matching on the Hypercube and Related Networks

E. W. Mayr, R. Werchner
1997 Algorithmica  
The algorithm is based on novel routing techniques and, for certain small subtrees, simulates optimal PRAM algorithms.  ...  For trees of size n, stored on a p processor hypercube in in-order, the running time of the algorithm is O( l n p m log p).  ...  One contribution of this paper is an optimal hypercube algorithm for the term alignment problem.  ... 
doi:10.1007/pl00009165 fatcat:65pjenki5fhole5albfvo6cw54

Divide-and-conquer algorithms on the hypercube

Ernst W Mayr, Ralph Werchner
1996 Theoretical Computer Science  
We give an optimal generic divide-and-conquer implementation on hypercubes for the class of divide-and-conquer algorithms for which the total size of the subproblems on any level of the recursion does  ...  Our results can also be applied to optimally solve various types of routing problems.  ...  permutations called parentheses-structured routings in logarithmic time on hypercubes.  ... 
doi:10.1016/0304-3975(96)00033-3 fatcat:mt7njgz4rnedzo73qz7ki7cz5a

An efficient mean field annealing formulation for mapping unstructured domains to hypercubes [chapter]

Cevdet Aykanat, Ismail Haritaoğlu
1995 Lecture Notes in Computer Science  
respectively, b y exploiting the topological properties of hypercubes.  ...  The proposed hypercube-speci c MFA f o r m ulation asymptotically reduces the number of spin variables and the computational complexity of an individual MFA iteration to Nlg2P and (davglg2P +Pl g 2P ),  ...  The proposed hypercube-speci c MFA formulation asymptotically reduces the number of spin variables and the complexity of the mean led computations compared to the general MFA f o r m ulation.  ... 
doi:10.1007/3-540-60321-2_9 fatcat:byidwkok4zafroqzytbkfcli5u

Comparative Evaluation of Adaptive and Deterministic Routing in the OTIS-Hypercube [chapter]

Hashem Hashemi Najaf-abadi, Hamid Sarbazi-Azad
2004 Lecture Notes in Computer Science  
In addition, the performance merits of adaptive wormhole routing in the OTIS-hypercube are compared with those of deterministic routing using extensive simulation experiments.  ...  In this paper, we propose an adaptive routing algorithm for the wormhole switched OTIS-hypercube.  ...  The address of each group is placed in parentheses above the group.  ... 
doi:10.1007/978-3-540-30102-8_29 fatcat:nsdeyjddyfgnljb6sitqdc7g5u

Routing and Broadcasting Algorithms for Generalized-Star Cube

Daiki Arai, Yamin Li
2016 International Journal of Networking and Computing  
International Journal of Networking and Computing and reduced hypercube [25] focused on the reduction of the number of links of the hypercube.  ...  The complexities of the routing and broadcasting algorithms are also examined.  ...  For these routing algorithms, we separate them into hypercube part and (n, k)-star graph part and use existing optimal algorithms.  ... 
doi:10.15803/ijnc.6.2_368 fatcat:daemiwcopnhknizxarfg2py5cy

A New Efficient Algorithm for Embedding an Arbitrary Binary Tree into Its Optimal Hypercube

Volker Heun, Ernst W. Mayr
1996 Journal of Algorithms  
In this paper, we present a simple one-to-one embedding of arbitrary binary trees into their optimal hypercubes with dilation 8 and constant congestion.  ...  On the other hand, the execution of many algorithms can be represented by binary trees, making desirable fast simulations of binary trees on hypercubes.  ...  There exists a one-to-one embedding of Q into its optimal hypercube with dilation 8 and constant congestion.  ... 
doi:10.1006/jagm.1996.0018 fatcat:6m5g34qsvnfmtd72b4pqazjvde

Odd even shifts in SIMD hypercubes

S. Ranka, S. Sahni
1990 IEEE Transactions on Parallel and Distributed Systems  
As an application, the algorithm is used to obtain an Ο(M 2 + logN) time and Ο(1) memory per processor algorithm to compute the two dimensional convolution of an N ×N image and an M ×M template on an N  ...  This improves the previous best complexity of Ο(M 2 logM + logN).  ...  [DEKE81] develop an optimal hypercube routing algorithm that begins with one data in each processor and circulates the collection of data through every processor such that each processor has only one  ... 
doi:10.1109/71.80126 fatcat:s6sq6k7o3jfv7l2fncqtxier3q

Scalable optical hypercube-based interconnection network for massively parallel computing

Ahmed Louri, Hongki Sung
1994 Applied Optics  
The OMMH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the torus (constant node degree and size scalability) networks  ...  For example, one of the most popular networks for paral-7588  ...  The authors are with the Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721.  ... 
doi:10.1364/ao.33.007588 pmid:20962964 fatcat:ov7p45y4bncppcgfrfonzw33xm

Reliable broadcasting in wormhole-routed hypercube-connected networks using local safety information

Dong Xiang, Ai Chen, Jie Wu
2003 IEEE Transactions on Reliability  
The sufficient condition for optimal broadcast of a message is presented in an unsafe hypercube. Extensive simulation results show that the proposed method outperforms previous methods, in all cases.  ...  An unsafe hypercube can be split into a set of maximal safe subcubes.  ...  The message can be broadcast optimally if the source is any one of 00000, 00010, 00011, 10 011. VI.  ... 
doi:10.1109/tr.2003.810071 fatcat:cizma5iewresjnx5bgk3o6xiau

Image template matching on MIMD hypercube multicomputers

Sanjay Ranka, Sartaj Sahni
1990 Journal of Parallel and Distributed Computing  
Efficient algorithms for image template matching on fine grained as well as medium grained MIMD hypercube multicomputers are developed.  ...  The medium grained MIMD algorithm is developed specifically for the NCUBE multicomputer. This algorithm is compared experimentally with an algorithm that is optimized for the Cray 2 supercomputer.  ...  These are approximately one fifth of the hypercube-to-hypercube times on the NCUBE/7 with 64 processors.  ... 
doi:10.1016/0743-7315(90)90008-d fatcat:326tnida7ne4pgm7i3vmbr2m3a

Clustering on a hypercube multicomputer

S. Ranka, S. Sahni
1991 IEEE Transactions on Parallel and Distributed Systems  
This is optimal up to a constant factor. We extend these results to the case when -Vd\fK processors are available. Experimental results from an MIMD medium grain hypercube are also presented.  ...  For a clustering problem with .V patterns, M features per pattern and I< clusters, our algorithms complete in O(k + logd%-dI) steps on S-ZI processor hypercubes.  ...  The number of unit routes required is 2 s . 7) Term Computation: This is done independently on all K x 1 column windows of the N M PE hypercube.  ... 
doi:10.1109/71.89059 fatcat:iy443xcyfjhhvksju6uwhgpvdm

Computing Hough transforms on hypercube multicomputers

Sanjay Ranka, Sartaj Sahni
1990 Journal of Supercomputing  
\Ve also consider the computation of the Hough transform on MIMD hypercubes ,vith a fixed number of processors. Experimental results on an NCUBE/7 hypercube are presented.  ...  Our algorithms can compute p angles of the Hough transform of an N x N image, P 5 N 1 in O(p + log N) time on both~1I~'1D and SIlv1D hypercubes. These algorithms require O(N2) processors.  ...  The fine grain algorithms are optimal and the algorithms for a medium grain hypercube exhibit n'ear-optimal speedups when load balancing is done. 31 are used to detect straight lines or edges in an image  ... 
doi:10.1007/bf00127879 fatcat:bdz3kl653zb5vjdeyohbhtnmna

Efficient Embeddings into Hypercube-like Topologies

V. Heun
2003 Computer journal  
In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs.  ...  The dilation and congestion of our embedding depends on the quality of the extended edge bisector.  ...  For λ = 0 the term in parentheses on the left-hand side of the first inequality is set to 1.  ... 
doi:10.1093/comjnl/46.6.632 fatcat:ywukz3e7n5defl5b6fzf3s5ime

Near-optimal broadcast in all-port wormhole-routed hypercubes using error-correcting codes

H. Ko, S. Latifi, P.K. Srimani
2000 IEEE Transactions on Parallel and Distributed Systems  
inside the parentheses correspond to the minimum Mg or sf= 4.  ...  on hypercube later in this section.  ... 
doi:10.1109/71.841741 fatcat:7pq4vyjip5bzdpa2jiiazgdmv4
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