A primal-simplex based Tardos' algorithm

In the mid-eighties Tardos proposed a strongly polynomial algorithm for solving linear programming problems for which the size of the coefficient matrix is polynomially bounded by the dimension. Combining Orlin's primal-based modification and Mizuno's use of the simplex method, we introduce a modification of Tardos' algorithm considering only the primal problem and using simplex method to solve the auxiliary problems. The proposed algorithm is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non-degenerate.Comment: 7 page

Studi Banding Kinerja Algoritma Optimasi Linier Model Primal dan Dual pada Persoalan SPOJ 27099 FN16ROAD-Road Times

Permasalahan dalam Tugas Akhir ini diambil dari dunia nyata namun sudah disederhanakan ke dalam bentuk soal yang terdapat pada situs Sphere Online Judge “FN16ROAD – Road Times”. Secara umum persoalan yang akan diselesaikan pada penelitian Tugas Akhir ini, dapat direpresentasikan sebagai persoalan optimasi linier. Metode penyelesaian yang dipilih adalah algoritma Simpleks. Algoritma Simpleks diimplementasikan pada dua model, yaitu model primal dan model dual. Dilakukan uji kebenaran pada hasil implementasi algoritma Simpleks pada model primal dan model dual. Kedua model tersebut kemudian dibandingkan kinerjanya baik dari segi waktu maupun memori. Algoritma Simpleks diimplementasikan dengan menggunakan bahasa pemrograman C++. Dari uji coba yang telah dilakukan, didapatkan kesimpulan bahwa algoritma yang dirancang telah sesuai dengan permasalahan ini. Model dual memiliki rata-rata waktu lebih baik dibandingkan model primal dengan selisih sebesar 2,007 detik. Sedangkan untuk rata-rata memori, model primal memiliki memori lebih kecil dibandingkan model dual dengan selisih sebesar 0,02 M. ================================================================================================================================ The problems in this Final Project are taken from the real world but have been simplified into the form of questions contained on the Sphere Online Judge site "FN16ROAD - Road Times". In general, the problems that will be solved in this Final Project research can be represented as linear optimization problems. The chosen settlement method is the Simplex algorithm. The Simplex algorithm is implemented in two models, namely the primal model and the dual model. The true test was conducted on the results of the implementation of the Simplex algorithm on the primal model and the dual model. The two models are then compared to their performance in terms of both time and memory. The Simplex algorithm is implemented using the C ++ programming language. From the trials that have been carried out, it was concluded that the algorithm was designed under this problem. The dual model has an average time better than the primal model with a difference of 2,007 seconds. As for the average memory, the primal model has a smaller memory than the dual model with a difference of 0.02 M