Comments on Integer Sorting on Sum-CRCW

Abstract- Given an array X of n elements from a restricted domain of integers [1, n]. The integer sorting problem is the rearrangement of n integers in ascending order. We study the first optimal deterministic sublogarithmic algorithm for integer sorting on CRCW PRAM. We give two comments on the algorithm. The first comment is the algorithm not runs in sublogarithmic time for any distribution of input data. The second comment is the cost of the algorithm is not linear. Then, we modify the algorithm to be optimal in sense of cost with a restriction on the input data. Our modification algorithm has time complexity log n n log log n O ( log log n) using log n Sum-CRCW processors. Also, the algorithm has linear space. I

(Extended Abstract)

Abstract — An addition sequence problem is given a set of numbers X = {n1, n2, · · · , nm}, what is the minimal number of additions needed to compute all m numbers starting from 1? Downey et al. [9] showed that the addition sequence problem is NPcomplete. This problem has application in evaluating the monomials y n1, y n2, · · · , y nm. In this paper, we present an algorithm to generate an addition sequence with minimal number of elements. We generalize some results on addition chain (m = 1) to addition sequence to speed up the computation

An Efficient Multicore Algorithm for Minimal Length Addition Chains

A minimal length addition chain for a positive integer m is a finite sequence of positive integers such that (1) the first and last elements in the sequence are 1 and m, respectively, (2) any element greater than 1 in the sequence is the addition of two earlier elements (not necessarily distinct), and (3) the length of the sequence is minimal. Generating the minimal length addition chain for m is challenging due to the running time, which increases with the size of m and particularly with the number of 1s in the binary representation of m. In this paper, we introduce a new parallel algorithm to find the minimal length addition chain for m. The experimental studies on multicore systems show that the running time of the proposed algorithm is faster than the sequential algorithm. Moreover, the maximum speedup obtained by the proposed algorithm is 2.5 times the best known sequential algorithm

Debugging Tool to Learn Algorithms: A Case Study Minimal Spanning Tree

This paper presents a visualization tool that works as a debugger to learn the minimal spanning tree. The tool allows the user to enter the graph as a matrix and then allow the user to visualize the execution of the algorithm step by step. During the visualization, the tool can handle and debug the errors that occurred by the user. Also the tool gives the user a feedback from the execution of the algorithm by storing the errors that occurred by the user. The tool can be used by the teacher and students inside and outside the class. The tool was evaluated by the students and the results show that the tool enhances the understanding of algorithms

Small Private Exponent Attacks on RSA Using Continued Fractions and Multicore Systems

The RSA (Rivest–Shamir–Adleman) asymmetric-key cryptosystem is widely used for encryptions and digital signatures. Let (n,e) be the RSA public key and d be the corresponding private key (or private exponent). One of the attacks on RSA is to find the private key d using continued fractions when d is small. In this paper, we present a new technique to improve a small private exponent attack on RSA using continued fractions and multicore systems. The idea of the proposed technique is to find an interval that contains ϕ(n), and then propose a method to generate different points in the interval that can be used by continued fraction and multicore systems to recover the private key, where ϕ is Euler’s totient function. The practical results of three small private exponent attacks on RSA show that we extended the previous bound of the private key that is discovered by continued fractions. When n is 1024 bits, we used 20 cores to extend the bound of d by 0.016 for de Weger, Maitra-Sarkar, and Nassr et al. attacks in average times 7.67 h, 2.7 h, and 44 min, respectively

Parallelizing exact motif finding algorithms on multi-core

The motif finding problem is one of the important and challenging problems in bioinformatics. A variety of sequential algorithms have been proposed to find exact motifs, but the running time is still not suitable due to high computational complexity of finding motifs. In this paper we parallelize three efficient sequential algorithms which are HEPPMSprune, PMS5 and PMS6. We implement the algorithms on a Dual Quad-Core machine using openMP to measure the performance of each algorithm. Our experiment on simulated data show that: (1) the parallel PMS6 is faster than the other algorithms in case of challenging instances, while the parallel HEPPMSprune is faster than the other algorithms in most of solvable instances; (2) the scalability of parallel HEPPMSprune is linear for all instances, while the scalability of parallel PMS5 and PMS6 is linear in case of challenging instances only; (3) the memory used by HEPPMSprune is less than that of the other algorithms.NPRP Grant No. 4-1454-1-233 from the Qatar National Research Fund (a member of Qatar Foundation).Scopu