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.

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.

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.

Parallel Algorithms for Listing Well-Formed Parentheses Strings

1998 ◽  
Vol 08 (01) ◽  
pp. 19-28 ◽  
Author(s):  
Vincent Vajnovszki ◽  
Jean Pallo
Keyword(s):  
Parallel Algorithms ◽  
Computational Model ◽  
Shared Memory ◽  
Linear Array ◽  
Lexicographic Order ◽  
Memory Location ◽  
Constant Delay ◽  
Crew Pram

We present two cost-optimal parallel algorithms generating the set of all well-formed parentheses strings of length 2n with constant delay for each generated string. In our first algorithm we generate in lexicographic order well-formed parentheses strings represented by bitstrings, and in the second one we use the representation by weight sequences. In both cases the computational model is based on an architecture CREW PRAM, where each processor performs the same algorithm simultaneously on a different set of data. Different processors can access the shared memory at the same time to read different data in the same or different memory locations, but no two processors are allowed to write into the same memory location simultaneously. These results complete a recent parallel generating algorithm for well-formed parentheses strings in a linear array of processors model, due to Akl and Stojmenović.

SYSTOLIC GENERATION OF COMBINATIONS FROM ARBITRARY ELEMENTS

1992 ◽  
Vol 02 (02n03) ◽  
pp. 241-248 ◽  
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.

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.

scholarly journals On a Positivity Conjecture in the Character Table of $S_n$

10.37236/8186 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Sheila Sundaram
Keyword(s):  
Lexicographic Order ◽  
Character Table ◽  
Power Sums ◽  
Special Cases ◽  
Schur Positive

In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$  or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$  Many new Schur positivity questions are 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.

A One-Phase Parallel Algorithm for the Sequence Alignment Problem

1998 ◽  
Vol 08 (04) ◽  
pp. 515-526 ◽  
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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