Sharmila Karim

Determining distinct circuit in complete graphs using permutation

A Half Butterfly Method (HBM) is a method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism. The Half Butterfly Method was applied in the field of combinatorics such as in listing permutations of n elements. However the method of determining distinct circuit using HBM for n > 4 is become tedious. Thus, in this paper, we present the method of generating distinct circuit using permutation.A Half Butterfly Method (HBM) is a method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism. The Half Butterfly Method was applied in the field of combinatorics such as in listing permutations of n elements. However the method of determining distinct circuit using HBM for n > 4 is become tedious. Thus, in this paper, we present the method of generating distinct circuit using permutation.

Some modifications of Sarrus’s rule method via permutation for finding determinant of 4 by 4 square matrix

Sarrus rule is well known method for finding determinant of square matrix. This method is also known as a cross multiplication method. However this method is not applicable for n > 3. With this motivation, we attempt to extend this method by employing some modifications using permutation for the case of 4 by 4 square matrix

Application of half butterfly method in listing permutation

A Half Butterfly Method is a new method introduced to construct the distinct circuits in complete graphs where used the concept of isomorphism. The Half Butterfly Method can be applied in the field of combinatorics such as in listing permutations of n elements. Thus, in this paper, we presented a permutation generation using Half Butterfly Method.

A variational discrete filled function approach in discrete global optimization

Many real-life applications governed by discrete variables poss multiple local optimal solutions, which requires the utilization of global optimization tools find the best solution amongst them. The main difficulty in determining the best solution, or also known as the global solution, is to escape from the basins surrounding local minimums. To overcome this issue, an auxiliary function is introduced in discrete filled function method which turns the local minimizer of the original function become a maximizer. Then, an improved local minimum is found by minimizing the filled function, otherwise the edge of the feasible region is attained. Based on a discrete filled function method from the literature, we propose a modification particularly on the neighbourhood search to enhance its computational efficiency. Numerical results suggest that the proposed algorithm is efficient in solving large scale complex discrete optimization problems.

Efficient parallel algorithm for listing permutation with Message Passing Interface (MPI)

An efficient parallel algorithm for a new permutation generation method is presented. The crucial task in our permutation generation algorithm is starter sets generation where listing n! permutation is dependent on starter sets. Thus the task of starter sets generation is partitioned. However the parallel algorithm with 12 initial starter sets is less efficient when numbers of processors are more than seven. For increasing performance of parallel algorithm over processors, the number of initial starter sets change to 60. This parallel algorithm is directly implemented from its sequential algorithm and integrated with Message Passing Interface (MPI) libraries. The improvement of the parallel algorithm is shown better performance in terms of speedup and efficiency.

A new method for starter sets generation by fixing any element

A new permutation technique based on distinct starter sets was introduced by employing circular and reversing operations. The crucial task is to generate the distinct starter sets by eliminating the equivalence starter sets. Meanwhile new strategies for starter sets generation without generating its equivalence starter sets were developed and more efficient in terms of computation time compared to old method. However all these algorithms have limitations in terms of fixing element to construct the first set (starter set) to begin with. It would be interesting to derive new strategy by fixing an element in any position. A new method is developed for starter sets generation namely STARSET1 based on circular where any element can be selected randomly to be fixed. The result showed that no redundancy of starter sets is occurring and no equivalence starter sets are obtained.

A permutation parallel algorithm under exchange restriction with message passing interface

The permutation generation method is based on starter sets generation under exchange operation and exploited it for listing down all n! Permutations. However permutation generation is time consuming process, the implementation of sequential algorithm to parallel computation is the option for reducing the computation time. The sequential algorithm is implemented to a parallel algorithm by integrating with Message Passing Interface (MPI) libraries by parallelizing the starter sets generation task. The speedup and efficiency is the indicator tool for analyzing performance of this parallel algorithm. The results show reduction time computation of parallel algorithm among processors.

An enumeration on the structure of nonrepeated triples in a three-fold triple system

The normally used method to construct three-fold triple system is idempotent latin squares. This existing method only produces three-fold triple system that has repeated triples. Thus, this paper attempts to propose a method for developing three-fold triple system that can generate nonrepeated triples in the design. We employ compatible factorization design to formulate the method for distinct three-fold triple system. In this method we need to ascertain a starter set as a first set to begin with. Further, we make use of this starter set to produce the design of distinct three-fold triple system. As special reference, we are keen to exemplify for case v = 9.

Complete graph K4 decomposition into circuits of length 4

This paper aims to propose a new method in decomposing K4 into circuits. Our method introduces two new strategies: Wing Strategy (WinS) and Endpoint Strategy (Endp-S). WinS contains first wing and second wing, while Endp-S contains first endpoint and second endpoint. The crucial task for generating circuits in WinS is two vertices of K4 are fixed to be the first wing, meanwhile in Endp-S, the vertices of the first wing are then put into the first endpoint, consecutively. Once the set of circuits are produced from these strategies, the drawing of that circuits can be obtained.

Improvement of parallel strategy for listing all permutations using starter sets

Non-equivalence starter sets are employed to generate permutations. The starter sets are obtained using exchange operation strategy. In order to reduce the computation time for listing all permutations, the starter sets are allocated to different processors so that the task can be performed in parallel. In this paper, an improved parallel strategy for distributing starter sets among processors is proposed. The numerical results reveal that this strategy not only improves the computation time but it also increases the efficiency of processors.