PARALLEL STRATEGY FOR STARTER SETS TO LIST ALL PERMUTATION BASED ON CYCLING RESTRICTION SHARMILA KARIM * , ZURNI OMAR, KHAIRIL ISKANDAR OTHMAN HASLINDA IBRAHIM Quantitative Sciences Building, Mathematics Department College of Arts and Sciences, Faculty of Information Technology and Universiti Utara Malaysia Quantitative Sciences, 06010 Sintok, Kedah, Malaysia Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia (mila * , zurni, linda)@uum.edu.my khairil@tmsk.uitm.edu.my ABSTRACT This paper presents a parallel implementation of a new permutation generation method. This permutation generation method is based on the starter sets for listing all the n! permutations. The sequential algorithm is developed and parallelized for parallel computing by integrating with Message Passing Interface (MPI) libraries. The performance of the parallel algorithms is presented to demonstrate the validation of the works. KEY WORDS Starter Sets, Permutation, Message Passing Interface (MPI), High Performance Computing (HPC) 1 INTRODUCTION Permutation generation is a time consuming operation for sequential algorithm. This difficulty can be overcome by using parallel computers with several processors running simultaneously. Numerous literatures had given attention in parallel algorithm for lexicographic order as stated and conducted in [2,6,8]. In spite of the lexicographic order, there were also works done on parallel algorithm in minimal change order [3], ranking and unranking [9], shuffling [4] and lower exceeding sequences [1]. These previous works were implemented in different diagrams such as linear array processor and vector computer where every processor was responsible for producing one element of every permutation generated and sharing data. Besides that, designing parallel algorithm for listing cases of the restricted or generalized permutation such as permutation with repetitions, cyclic permutations, rosary permutations, alternate permutations, and linear extension still remain as open problems [2, 13]. Since our sequential algorithm for permutation generation is based on cycling restriction, we enhance our algorithm for parallel computing. Our algorithm will be implemented in distributed-shared memory computer with Message Passing Interface. MPI connected by an interconnection network global shared memory [10]. Message Passing is a powerful for general method of expressing parallelism [11, 12] The numerical tests in this research are performed on the Sunfire 1280 High Performance Computer, INSPEM, UPM. The Sunfire V1280 HPC is a MIMD distributed shared memory multiprocessor