A SIMPLE OPTIMAL SYSTOLIC ALGORITHM FOR GENERATING PERMUTATIONS

We describe a simple parallel algorithm for generating all permutations of n elements. The algorithm is designed to be executed on a linear array of n processors, each having constant size memory and each being responsible for producing one element of a given permutation. There is a constant delay per permutation, leading to an O (n!) time solution. The algorithm is cost-optimal, assuming the time to output the permutations is counted.

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SYSTOLIC GENERATION OF COMBINATIONS FROM ARBITRARY ELEMENTS

Parallel Processing Letters ◽

10.1142/s0129626492000374 ◽

1992 ◽

Vol 02 (02n03) ◽

pp. 241-248 ◽

Cited By ~ 3

Author(s):

HASSAN ELHAGE ◽

IVAN STOJMENOVIĆ

Keyword(s):

Linear Array ◽

Constant Delay ◽

Constant Size ◽

Time Solution ◽

Systolic Algorithm

A systolic algorithm is described for generating, in lexicographically ascending order, all combinations of m objects chosen from an arbitrary set of n elements. The algorithm is designed to be executed on a linear array of m processors, each having constant size memory (except processor m, which has O(n) memory), and each being responsible for producing one element of a given combination. There is a constant delay per combination, leading to an O (C(m, n)) time solution, where C(m, n) is the total number of combinations. The algorithm is cost-optimal (assuming the time to output the combinations is counted), and does not deal with very large integers.

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CONSTANT DELAY PARALLEL COUNTERS

Parallel Processing Letters ◽

10.1142/s0129626491000094 ◽

1991 ◽

Vol 01 (02) ◽

pp. 143-148 ◽

Cited By ~ 4

Author(s):

SELIM G. AKL ◽

THIBAULT DUBOUX ◽

IVAN STOJMENOVIC

Keyword(s):

Parallel Algorithm ◽

Linear Array ◽

Lexicographic Order ◽

Constant Delay ◽

Constant Size ◽

Special Cases

We present a cost-optimal parallel algorithm for generating variations of m elements out of {0, 1, …, n - 1} in lexicographic order. It uses a linear array of m processors, each having constant size memory and each being responsible for producing one part of a given variation. Binary and decimal counters are special cases of the algorithm, when n = 2 and n = 10, respectively. To our knowledge, the algorithm presented here is the first to be published with the property that the delay between any two variations generated is constant.

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GENERATING n-ARY REFLECTED GRAY CODES ON A LINEAR ARRAY OF PROCESSORS

Parallel Processing Letters ◽

10.1142/s0129626496000042 ◽

1996 ◽

Vol 06 (01) ◽

pp. 27-34 ◽

Cited By ~ 7

Author(s):

IVAN STOJMENOVIC

Keyword(s):

Parallel Algorithm ◽

Arbitrary Number ◽

Linear Array ◽

Gray Code ◽

Gray Codes ◽

Model Of Computation ◽

Constant Size

We present a cost-optimal parallel algorithm for generating n-ary reflected Gray codes, i.e. variations of m elements out of {0, 1,…, n–1} in a Gray code order. It uses a linear array of m processors, each having constant size memory and each being responsible for producing one part of a given variation. The algorithm is simple and uses a weaker model of computation than a recently published algorithm. In addition, it can be made adaptive (i.e. to run on a linear array with an arbitrary number of processors) and can be generalized to produce variations out of an arbitrary set of elements.

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A One-Phase Parallel Algorithm for the Sequence Alignment Problem

Parallel Processing Letters ◽

10.1142/s012962649800050x ◽

1998 ◽

Vol 08 (04) ◽

pp. 515-526 ◽

Cited By ~ 4

Author(s):

Thierry Lecroq ◽

Jean-Frederic Myoupo ◽

David Seme

Keyword(s):

Parallel Algorithm ◽

Sequence Alignment ◽

Edit Distance ◽

Linear Array ◽

Systolic Algorithm ◽

Alignment Problem

This paper introduces a new linear systolic algorithm [10] for the sequence alignment problem [18]. It is made up of min(n, m) processors and computes the edit distance and the sequence alignment of two sequences Target and Source in time min(n, m) + 2.max(n, m), where n and m denote the lengths of Target and Source respectively. Its characteristics make it faster and more efficient than the previous linear array algorithm for the alignment search.

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DESIGNING A SYSTOLIC ALGORITHM FOR GENERATING WELL-FORMED PARENTHESIS STRINGS

Parallel Processing Letters ◽

10.1142/s0129626404001738 ◽

2004 ◽

Vol 14 (01) ◽

pp. 83-97

Author(s):

JONG-CHUANG TSAY

Keyword(s):

Linear Array ◽

Vlsi Implementation ◽

Processor Array ◽

Lexicographical Order ◽

Systolic Algorithm ◽

Left And Right ◽

Local Connection

A parenthesis string is a string of left and right parentheses. The string is well-formed when it consists of balanced pairs of left and right parentheses. This study presents a novel systolic algorithm for generating all the well-formed parenthesis strings in lexicographical order. The algorithm is cost-optimal and is run on a linear array of processors such that each well-formed parenthesis string can be generated in three time steps. The processor array is appropriate for VLSI implementation, since it has the features of modularity, regularity, and local connection.

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A PARALLEL ALGORITHM TO GENERATE N-ARY REFLECTED GRAY CODES IN A LINEAR ARRAY WITH RECONFIGURABLE BUS SYSTEM

Parallel Processing Letters ◽

10.1142/s0129626493000198 ◽

1993 ◽

Vol 03 (02) ◽

pp. 157-164 ◽

Cited By ~ 2

Author(s):

P. THANGAVEL ◽

V.P. MUTHUSWAMY

Keyword(s):

Parallel Algorithm ◽

Linear Array ◽

Constant Time ◽

Processor Array ◽

Gray Codes ◽

System A ◽

Processor Arrays ◽

Bus System

A simple parallel algorithm for generating N-ary reflected Gray codes is presented. The algorithm is derived from the pattern of N-ary reflected Gray codes. The algorithm runs on a linear processor array with a reconfigurable bus system. A reconfigurable bus system is a bus system whose configuration can be dynamically changed. Recently processor arrays with reconfigurable bus systems were used to solve many problems in constant time. There already exists experimental reconfigurable chips.

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A parallel algorithm for mapping a special class of task graphs onto linear array multiprocessors

Proceedings of the 1994 ACM symposium on Applied computing - SAC '94 ◽

10.1145/326619.326815 ◽

1994 ◽

Author(s):

Sibabrata Ray ◽

Hong Jiang ◽

Jitender S. Deogun

Keyword(s):

Parallel Algorithm ◽

Special Class ◽

Linear Array ◽

Task Graphs

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TWO ALGORITHMS FOR COMPUTING THE EUCLIDEAN DISTANCE TRANSFORM

International Journal of Image and Graphics ◽

10.1142/s0219467801000359 ◽

2001 ◽

Vol 01 (04) ◽

pp. 635-645 ◽

Cited By ~ 5

Author(s):

MARINA L. GAVRILOVA ◽

MUHAMMAD H. ALSUWAIYEL

Keyword(s):

Parallel Algorithm ◽

Euclidean Distance ◽

Linear Array ◽

Linear Time ◽

Sequential Algorithm ◽

Distance Transform ◽

Optimal Algorithms ◽

Euclidean Metric ◽

Input Size ◽

Feature Transform

Given an n × n binary image of white and black pixels, we present two optimal algorithms for computing the distance transform and the nearest feature transform using the Euclidean metric. The first algorithm is a fast sequential algorithm that runs in linear time in the input size. The second is a parallel algorithm that runs in O(n2/p) time on a linear array of p processors, p, 1 ≤ p ≤ n.

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