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

1996 ◽  
Vol 06 (01) ◽  
pp. 27-34 ◽  
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.

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

1993 ◽  
Vol 03 (02) ◽  
pp. 157-164 ◽  
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.

A SIMPLE OPTIMAL SYSTOLIC ALGORITHM FOR GENERATING PERMUTATIONS

1992 ◽  
Vol 02 (02n03) ◽  
pp. 231-239 ◽  
Author(s):  
SELIM G. AKL ◽  
IVAN STOJMENOVIĆ
Keyword(s):  
Parallel Algorithm ◽  
Linear Array ◽  
Constant Delay ◽  
Constant Size ◽  
Time Solution ◽  
Systolic Algorithm

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.

CONSTANT DELAY PARALLEL COUNTERS

1991 ◽  
Vol 01 (02) ◽  
pp. 143-148 ◽  
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.

scholarly journals Permutational labelling of constant weight Gray codes

2002 ◽  
Vol 65 (3) ◽  
pp. 399-406
Author(s):  
Inessa Levi ◽  
Steve Seif
Keyword(s):  
Gray Code ◽  
Gray Codes ◽  
Constant Weight ◽  
Single Exception ◽  
Positive Integers

We prove that for positive integers n and r satisfying 1 < r < n, with the single exception of n = 4 and r = 2, there exists a constant weight Gray code of r-sets of Xn = {1, 2, …, n} that admits an orthogonal labelling by distinct partitions, with each subsequent partition obtained from the previous one by an application of a permutation of the underlying set. Specifically, an r-set A and a partition π of Xn are said to be orthogonal if every class of π meets A in exactly one element. We prove that for all n and r as stated, and taken modulo , there exists a list of the distinct r-sets of Xn with |Ai ∩ Ai+1| = r − 1 and a list of distinct partitions such that πi is orthogonal to both Ai and Ai+1, and πi+1 = πiλi for a suitable permutation λi of Xn.

On the exhaustive generation of generalized ballot sequences in lexicographic and Gray code order

2019 ◽  
Vol 28 (1) ◽  
pp. 109-119
Author(s):  
Ahmad Sabri ◽  
Vincent Vajnovszki
Keyword(s):  
Positive Integer ◽  
Gray Code ◽  
Lexicographic Order ◽  
Gray Codes ◽  
Fixed Length ◽  
Generating Algorithms

Abstract A generalized (resp. p-ary) ballot sequence is a sequence over the set of non-negative integers (resp. integers less than p) where in any of its prefixes each positive integer i occurs at most as often as any integer less than i. We show that the Reected Gray Code order induces a cyclic 3-adjacent Gray code on both, the set of fixed length generalized ballot sequences and p-ary ballot sequences when p is even, that is, ordered list where consecutive sequences (regarding the list cyclically) differ in at most 3 adjacent positions. Non-trivial efficient generating algorithms for these ballot sequences, in lexicographic order and for the obtained Gray codes, are also presented.

TWO ALGORITHMS FOR COMPUTING THE EUCLIDEAN DISTANCE TRANSFORM

2001 ◽  
Vol 01 (04) ◽  
pp. 635-645 ◽  
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.

scholarly journals Binary Gray Codes with Long Bit Runs

10.37236/1720 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Luis Goddyn ◽  
Pavol Gvozdjak
Keyword(s):  
Hamming Distance ◽  
Gray Code ◽  
Gray Codes

We show that there exists an $n$-bit cyclic binary Gray code all of whose bit runs have length at least $n - 3\log_2 n$. That is, there exists a cyclic ordering of $\{0,1\}^n$ such that adjacent words differ in exactly one (coordinate) bit, and such that no bit changes its value twice in any subsequence of $n-3\log_2 n$ consecutive words. Such Gray codes are 'locally distance preserving' in that Hamming distance equals index separation for nearby words in the sequence.

scholarly journals A Less Complex Algorithmic Procedure for Computing Gray Codes

2009 ◽  
Vol 6 (2) ◽  
pp. 12 ◽  
Author(s):  
Afaq Ahmad ◽  
Mohammed M. Bait Suwailam
Keyword(s):  
Boolean Function ◽  
Gray Code ◽  
Gray Codes ◽  
Time And Space ◽  
Design And Implementation ◽  
Algorithmic Procedure

 The purpose of this paper is to present a new and faster algorithmic procedure for generating the n bi Gray codes. Thereby, through this paper we have presented the derivation, design and implementation of a newly developed algorithm for the generation of an n-bit binary reflected Gray code sequences. The developed algorithm is stemmed from the fact of generating and properly placing the min-terms from the universal set of all the possible min-terms [m0 m1 m2 …. mN] of Boolean function of n variables, where, 0 < N <  2n-1. The resulting algorithm is in concise form and trivial to implement. Furthermore, the developed algorithm is equipped with added attributes of optimizing of time and space while executed. 

scholarly journals Gray codes and overlap cycles for restricted weight words

2014 ◽  
Vol 06 (04) ◽  
pp. 1450062
Author(s):  
Victoria Horan ◽  
Glenn Hurlbert
Keyword(s):  
Gray Code ◽  
Existence Results ◽  
Minimal Change ◽  
Gray Codes ◽  
Weight Range ◽  
Combinatorial Objects ◽  
The Past ◽  
Fixed Weight ◽  
New Type ◽  
Overlap Cycles

A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been considered in the past, we provide a new, simple Gray code for fixed-weight m-ary strings. In addition, we consider a relatively new type of Gray code known as overlap cycles and prove basic existence results concerning overlap cycles for fixed-weight and weight-range m-ary words.

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