Judul: Karakterisasi Morfologi Lima Populasi Nanas (Ananas Comosus (L.) Merr.)
Abstrak: Indonesia memiliki berbagai macam kultivar nanas yang telah dibudidayakan oleh para petani mulai Sumatra sampai Irian Jaya. Nanas dapat tumbuh di wilayah dengan tipe agroklimat yang berbeda-beda mulai dari dataran tinggi sampai dataran rendah. Daerah penghasil buah nanas adalah Palembang, Riau, Jambi, Bogor, Subang, Pandeglang, Tasikmalaya, dan Kutai. Buah nanas sudah menjadi trademark bagi suatu daerah atau wilayah. Salah satu permasalahan pengembangan buah nanas di Indonesia menuju arah yang lebih baik yaitu kurangnya informasi tentang karakteristik morfologi pertumbuhan maupun kandungan kimia buah nanas yang diusahakan oleh petani nanas seperti nanas Bogor, Minyak, Buaya, Merah, dan Hijau. Nanas-nanas tersebut kemungkinan mempunyai potensi unggul untuk industri pengolahan maupun konsumsi buah segar.
Keyword: 

Judul: Karakteristik morfologi da kualitas buah nenas (Ananas comosus (L.) Merr.) dari empat populasi di kecamatan Cijeruk kabupaten Bogor
Abstrak: Nenas merupakan salah satu buah tropika yang cukup popular di Indonesia walaupun tanaman ini bukanlah tanaman asli Indonesia. Dilihat dari perbedaan ukuran tanaman dan buah, warna dan rasa daging buah, kultivar nenas dibedakan menjadi beberapa kultivar yaitu nenas cayene, nenas Queen, nenas Spanish, nenas Abacaci dan nenas Maipure. Di Indonesia salah satu kultivar nenas yang diproduksi adalah nenas Queen dan salah satu daerah yang memproduksinya adalah Bogor, Jawa Barat.
Keyword: 

Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm