Filters








15,050 Hits in 3.6 sec

An exact, cache-localized algorithm for the sub-quadratic convolution of hypercubes [article]

Oliver Serang
2016 arXiv   pre-print
Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms  ...  Embeddings in hypercubes can be paired with sub-quadratic hypercube convolution method to construct sub-quadratic algorithms for variants of vector convolution.  ...  This means that max-convolution on hypercubes containing integers of bounded dynamic range can be performed exactly by using a value of p large enough that the relative error 1 − N −1 p drops low enough  ... 
arXiv:1608.00206v1 fatcat:bhqmio2ubvesxflce5ds4dj6le

Page 3948 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
An efficient multiple-copy embedding of the cube-connected-cycles network within the hypercube is presented.  ...  In this paper a new technique is presented for mapping computa- tions into hypercubes. The method used speeds up the transfer of a large amount of data.  ... 

Fast, deterministic routing, on hypercubes, using small buffers

B.C. Kuszmaul
1990 IEEE transactions on computers  
We identify nodes with integers by using the standard numbering scheme for a hypercube.  ...  On the other hand, it is very hard to build hypercubes of very large numbers of nodes, which indicates that we may never reach the point where the constants involved become unimportant.  ... 
doi:10.1109/12.61048 fatcat:2joyondogbfydm3b3qd2maiw5i

Liminf Sets in Simultaneous Diophantine Approximation

Faustin Adiceam
2016 Journal de Théorie des Nombres de Bordeaux  
On the logarithmic density of a subset of integers.  ...  One key-step in the proof of Theorem 1.1 is to approximate an infinite set of positive integers by arbitrarily large subsets, the size of a subset being measured by its exponent of convergence.  ...  only by integer vectors (r, q) such that q is a multiple of the integer p provided it is large enough.  ... 
doi:10.5802/jtnb.949 fatcat:oct7mjvhwfeq7fi6p2mmxj5jti

Liminf Sets in Simultaneous Diophantine Approximation [article]

Faustin Adiceam
2013 arXiv   pre-print
Let Q be an infinite set of positive integers.  ...  of µ k on each of these hypercubes being uniform.  ...  One key-step in the proof of Theorem 1 is to approach an infinite set of positive integers by arbitrarily large subsets, the size of a subset being measured by its exponent of convergence.  ... 
arXiv:1308.3806v1 fatcat:zhdjhbmw3rgyxat4wtpakrppiu

Vertex Ramsey Problems in the Hypercube

John Goldwasser, John Talbot
2012 SIAM Journal on Discrete Mathematics  
If we 2-color the vertices of a large hypercube what monochromatic substructures are we guaranteed to find?  ...  A key tool is a lemma which reduces questions concerning monochromatic configurations in the hypercube to questions about monochromatic translates of sets of integers.  ...  The integer c L (s, t) produced by this "tower of Ramsey numbers" is obviously rather large if s is large.  ... 
doi:10.1137/110832239 fatcat:n5iobe67yracpovkmrle2pjju4

Vertex Ramsey problems in the hypercube [article]

John Goldwasser, John Talbot
2012 arXiv   pre-print
If we 2-color the vertices of a large hypercube what monochromatic substructures are we guaranteed to find?  ...  A key tool is a lemma which reduces questions concerning monochromatic configurations in the hypercube to questions about monochromatic translates of sets of integers.  ...  The integer c L (s, t) produced by this "tower of Ramsey numbers" is obviously rather large if s is large.  ... 
arXiv:1211.0168v1 fatcat:tybb3ztlmnfozihdg2gedifon4

Decomposing the vertex set of a hypercube into isomorphic subgraphs [article]

Vytautas Gruslys
2016 arXiv   pre-print
Let G be an induced subgraph of the hypercube Q_k for some k. We show that if |G| is a power of 2 then, for sufficiciently large n, the vertex set of Q_n can be partitioned into induced copies of G.  ...  In fact, we prove a stronger statement: if X is a subset of {0,1}^k for some k and if |X| is a power of 2, then, for sufficiently large n, {0,1}^n can be partitioned into isometric copies of X.  ...  Let F and S be as above and let r be a positive integer. We say that F contains an r-partition of S if there exists a weight function on F for which every element of S has multiplicity r.  ... 
arXiv:1611.02021v1 fatcat:prcn5wvm5jhmrhnarn7o3jm3sa

MIMD-Factorisation on hypercubes [chapter]

F. Damm, F. -P. Heider, G. Wambach
1995 Lecture Notes in Computer Science  
This paper describes the development and implementation of the MPQS factoring algorithm using multiple hypercubes customised to a MIMD parallel computer.  ...  The computationally most expensive steps ran on a Parsytec machine consisting of 1024 Inmos T805 microprocessors. General 100 decimal digit numbers can be factored in 1-2 days.  ...  MPQS on a Hypercube We assume familiarity with the 'Multiple Polynomial Quadratic Sieve' (MPQS) algorithm [8, 11] and will sketch only the improved hypercube variation used by US.  ... 
doi:10.1007/bfb0053454 fatcat:hvjzwjliknhddctlqc2munml3y

Page 3202 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Our se- quence corresponds to a Hamiltonian path on the n-dimensional hypercube C,,, where n is @(log N/loglog N).  ...  This yields a faster way of changing polynomials in the multiple polynomial quadratic sieve algorithm, since moving along the hypercube turns out to be very cheap.”  ... 

On the Density of Integer Points on the Generalised Markoff-Hurwitz and Dwork Hypersurfaces [article]

Igor E. Shparlinski
2014 arXiv   pre-print
We use bounds of mixed character sums modulo a prime p to estimate the density of integer points on the hypersurface f_1(x_1) + ... + f_n(x_n) =a x_1^k_1... x_n^k_n for some polynomials f_i ∈ Z[X], nonzero  ...  integer a and positive integers k_i i=1, ..., n.  ...  Let ν ≥ 1 be a fixed integer. Then for a sufficiently large positive integer T ≥ 3, for all but o(π(T )) primes p ≤ T and any integers u and h < p, we have the bound 1) .  ... 
arXiv:1404.5866v1 fatcat:gg3mngpzq5gubgl677hell44k4

Edge Sums Of De Bruijn Interconnection Networks

Daniela Ferrero, Frank Harary
2003 International Journal of Computer Mathematics  
This problem was introduced by Graham and Harary who presented the solution for hypercubes.  ...  An interconnection network is a highly symmetrical connected graph of order n nodes, size m edges, connectivity k and diameter d, where n and k are large but m and d are small.  ...  The hypercube Q n has for its nodes the set V n of all the binary sequences with n terms, two of which are adjacent whenever the sequences disagree in exactly one place.  ... 
doi:10.1080/0020716031000087159a fatcat:x7phmarbhfbzbah4o54rk4dlvm

On the Achromatic Number of Hypercubes

Yuval Roichman
2000 Journal of combinatorial theory. Series B (Print)  
For an m-dimensional hypercube P m 2 we prove: There exist constants 0 < c 1 < c 2 , independent of m, such that c 1 (m2 m?1 ) 1=2 (P m 2 ) c 2 (m2 m?1 ) 1=2 :  ...  The achromatic number of a nite graph G, (G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge.  ...  The following theorem determines the achromatic number of a hypercube of a suciently large dimension up to a multiplication by a constant. Theorem 3. For a hypercube of dimension d, Q d : (2 ?  ... 
doi:10.1006/jctb.2000.1955 fatcat:fg6cticnzzeg3fjydmlnv3znfy

Decremental Scattering for Data Transport Between Host and Hypercube Nodes

Mukesh Sharma, Meghanad D. Wagh
1993 1993 International Conference on Parallel Processing - ICPP'93 Vol2  
This strategy, based on scatteeng on hypercubes of decremental dimemiom, p e r f o r m much better than other sirraiegies known today.  ...  In this paper we study a new strategy for data: distribuUonfiom host to MIMD hypercube nodes.  ...  In this paper we derive a new strategy for host to hypercube node communication based on multiple communications from host to decreasing dimension hypercubea.  ... 
doi:10.1109/icpp.1993.67 dblp:conf/icpp/SharmaW93 fatcat:3sg4knszcrfi5ivvxik24nfshi

Hybrid Parallel Bidirectional Sieve based on SMP Cluster [article]

Gang Liao, Lian Luo, Lei Liu
2012 arXiv   pre-print
The approach obtains huge speedup and efficiency on SMP Cluster.  ...  article, hybrid parallel bidirectional sieve method is implemented by SMP Cluster, the individual computational units joined together by the communication network, are usually shared-memory systems with one  ...  As n gets large, an algorithm with exponential complexity quickly becomes impractical.  ... 
arXiv:1205.4883v1 fatcat:542sc5zinzgshmwfuxz26uls3u
« Previous Showing results 1 — 15 out of 15,050 results