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Page 589 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

Summary: “A

*systolic**algorithm*is described*for**generating*,*in**lexicographically*ascending*order*, all combinations of m objects chosen from {1,---,”}. ... Dymacek (1-WLEE) 93b:05010 93b:05006 05A05 05-04 65Y05 Stojmenovié, Ivan (3-OTTW-C) A simple*systolic**algorithm**for**generating*combinations*in**lexicographic**order*. Comput. Math. ...##
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Page 1643 of Mathematical Reviews Vol. , Issue 94c
[page]

1994
*
Mathematical Reviews
*

Summary: “A

*systolic**algorithm*is described*for**generating*,*in**lexicographically*ascending*order*, all combinations of m objects chosen from*an*arbitrary set of n elements. ... Stojmenovic¢, Ivan (3-OTTW-C; Ottawa, ON) A simple*optimal**systolic**algorithm**for**generating**permutations*. ...##
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Listing combinatorial objects in parallel

2006
*
International Journal of Parallel, Emergent and Distributed Systems
*

This article surveys parallel

doi:10.1080/17445760500355777
fatcat:hyv74hfce5akdczakpibqb5adq
*generation**algorithms**for*listing all combinatorial objects of certain type. The*algorithms*are designed*for*a very simple model, linear array of processors. ... How to design*an**algorithm**for**generating*set partitions that will satisfy Properties 1 -6 (*in**lexicographic*or other*order*)? ... It is*an*open problem to design parallel*algorithms**for*listing the following cases of the restricted or*generalized**permutations*:*permutations*of m out of n elements*in**lexicographic**order*,*permutations*...##
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SYSTOLIC GENERATION OF COMBINATIONS FROM ARBITRARY ELEMENTS

1992
*
Parallel Processing Letters
*

A

doi:10.1142/s0129626492000374
fatcat:w6gpyyxnffcibisq5ezgvb5hxq
*systolic**algorithm*is described*for**generating*,*in**lexicographically*ascending*order*, all combinations of rn o$ects chosen from*an*arbitrary set of n elements. ... The 'lgorithm is cost-*optimal*(assuming the time to output the combinations is counted), a,nd does not deal with very large integers, Kellwoxbt Combinations, linear array of processors,*generating*combinatorial ... There exist*algorithms**for**generating**permutations*[24] and derangements [25] satisfying criteria (1)-(6). ...##
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A data locality optimizing algorithm

2004
*
SIGPLAN notices
*

Our paper "A Data Locality

doi:10.1145/989393.989437
fatcat:eajlltosg5gjbhqtdituqhh3hi
*Optimizing**Algorithm*" presented*an*automatic blocking*algorithm**for*perfect loop nests on uniprocessors and multiprocessors [8] . ...*In*each of my attempts to*optimize*data locality, first with Michael Wolf then with Amy Lim, we ended up finding*an**algorithm**for*parallelization first before solving the locality problem. ...##
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FPGA Generators of Combinatorial Configurations in a Linear Array Model

2008
*
2008 International Symposium on Parallel and Distributed Computing
*

*For*implementation several

*systolic*

*algorithms*were selected that

*generate*combinatorial configurations

*in*a linear array model. ...

*In*this paper we describe hardware implementations of

*generators*of combinatorial objects. ... Acknowledgements The research was supported

*in*part by a research grant number E-7/423/BW/2008 obtained from CUT by the first author. ...

##
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A data locality optimizing algorithm

1991
*
SIGPLAN notices
*

Our paper "A Data Locality

doi:10.1145/113446.113449
fatcat:2ovh6wjxmjhorne6ox3dlj47ha
*Optimizing**Algorithm*" presented*an*automatic blocking*algorithm**for*perfect loop nests on uniprocessors and multiprocessors [8] . ...*In*each of my attempts to*optimize*data locality, first with Michael Wolf then with Amy Lim, we ended up finding*an**algorithm**for*parallelization first before solving the locality problem. ...##
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On Parallel Generation of t—Ary Trees in an Associative Model
[chapter]

2002
*
Lecture Notes in Computer Science
*

*In*this paper a new parallel

*algorithm*is presented

*for*

*generation*of t-ary trees. Computations run

*in*

*an*associative processor model. ... Tree sequences are

*generated*

*in*

*lexicographic*

*order*, with O(1) time per object,

*in*a new representation, as combinations with repetitions with restricted growth. ...

*Algorithm*TREEGEN

*generates*,

*in*the form of t-sequences, all t-ary trees with n internal nodes

*in*the

*lexicographic*

*order*with constant time per tree

*in*

*an*associative model with n+1 processors, each of ...

##
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Synthesizing transformations for locality enhancement of imperfectly-nested loop nests

2014
*
25th Anniversary International Conference on Supercomputing Anniversary Volume -
*

We present

doi:10.1145/2591635.2667179
fatcat:x3uqhtqh55exzd6guuapwahiui
*an*approach*for*synthesizing transformations to enhance locality*in*imperfectly-nested loops. ... The product space is then transformed further to enhance locality, after which fully*permutable*loops are tiled, and code is*generated*. ... Figure 11 shows*an**algorithm*that finds a nearby legal*permutation*. ...##
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Synthesizing transformations for locality enhancement of imperfectly-nested loop nests

2000
*
Proceedings of the 14th international conference on Supercomputing - ICS '00
*

We present

doi:10.1145/335231.335245
dblp:conf/ics/AhmedMP00
fatcat:kwkqtl4zujbq7izrjrrmaafpim
*an*approach*for*synthesizing transformations to enhance locality*in*imperfectly-nested loops. ... The product space is then transformed further to enhance locality, after which fully*permutable*loops are tiled, and code is*generated*. ... Figure 11 shows*an**algorithm*that finds a nearby legal*permutation*. ...##
###
Dual Super-Systolic Core for Real-Time Reconstructive Algorithms of High-Resolution Radar/SAR Imaging Systems

2012
*
Sensors
*

As

doi:10.3390/s120302539
pmid:22736964
pmcid:PMC3376574
fatcat:rh3ohzgyabfvngoam3enitca6m
*an*implementation test case, the proposed approach was aggregated*in*a HW/SW co-design scheme*in**order*to solve the nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial ... A high-speed dual super-*systolic*core*for*reconstructive signal processing (SP) operations consists of a double parallel*systolic*array (SA) machine*in*which each processing element of the array is also ...*For*the loop*permutation*, the following unimodular transformation 0 1 1 0 ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ P T was applied*in**order*to*permute*the index-space of the locally recursive*algorithm*The source Polytope is described ...##
###
Page 1661 of Mathematical Reviews Vol. , Issue 91C
[page]

1991
*
Mathematical Reviews
*

It was proved by Kolmogorov that

*for*any set S there exists*an**optimal*coding of S (*in**an*appropriately defined way). ...*An*interesting feature of this*algorithm*is that it finds a highest-level-first schedule: such a schedule defines a*lexicographically*first solution to this problem*in*a natural way. ...##
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Transformations for imperfectly nested loops

1996
*
Proceedings of the 1996 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '96
*

Our approach is

doi:10.1145/369028.369051
fatcat:i6sbfqwc3rgw5f2r5ioesei4eq
*an*extension of the linear loop transformation framework*for*perfectly nested loops, and it models*permutation*, reversal, skewing, scaling, alignment, distribution and jamming. ...*In*this paper, we present*an*approach to transforming imperfectly nested loops directly. ...*In*this paper, we present*an*approach to transforming imperfectly nested loops that trades o*generality**for*simplicity. ...##
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Constraint directed CAD tool for automatic latency-optimal implementation of 1-D and 2-D Fourier transforms

2002
*
Reconfigurable Technology: FPGAs and Reconfigurable Processors for Computing and Communications IV
*

A specialized CAD tool is described that will take a user's high level code description of a non-uniform affinely indexed

doi:10.1117/12.455338
fatcat:jcwzawy755c3nleaxxqfcwbvye
*algorithm*and automatically*generate*abstract latency-*optimal**systolic*arrays. ... The tool is then used to*generate*new 1-D and 2-D hardware efficient*systolic*arrays*for*the discreet Fourier transform that take advantage of the use of the radix-4 matrix decomposition. ...*In**order*to achieve better throughputs SPADE was used to*generate*more regular solutions with sub-*optimal*areas by setting the secondary objective function to look*for*maximum regularity arrays. ...##
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Hardware synthesis for systems of recurrence equations with multidimensional schedule

2008
*
International Journal of Embedded Systems
*

We explain how to combine the allocation and memory functions

doi:10.1504/ijes.2008.022398
fatcat:frxv6j57dnduvke57hk5jnhxxa
*in**order*to meet the computer owns rule, and we present*an*original mechanism*for*controlling the operation of the architecture. ... This paper introduces methods*for*extending the classical*systolic*synthesis methodology to multidimensional time. ...*In*any given processor, it*generates**an*enable signal*for*each variable. ...
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