Judul: Teknik Perbanyakan dan Kekerabatan Genetik Pasak Bumi (Eurycoma longifolia Jack)
Abstrak: Indonesia sebagai salah satu negara megabiodiversity yang diperkirakan memiliki 30.000 tumbuhan dan sekitar 1260 spesies di antaranya berkhasiat sebagai obat. Sampai saat ini baru sekitar 180 spesies yang telah digunakan untuk berbagai keperluan industri obat dan jamu, tetapi hanya beberapa spesies saja yang telah dibudidayakan secara intensif (Supriadi 2001).
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Judul: Teknik Perbanyakan dan Kekerabatan Genetik Pasak Bumi (Eurycoma longifolia Jack)
Abstrak: Pasak bumi (Eurycoma longifolia Jack) is a shrubs growing wildly in the forests of Southeast Asia and widely used throughout the region because of its medicinal properties. Uncontrolled harvesting of wild-grown trees has led to rapid decrease of natural populations, as well as causing a potential decrease in genetic diversity. The objectives of this research were 1). To get information about propagation technique of pasak bumi by seed and stem cutting and its suitable growing medium and 2). To estimate genetic relatedness of pasak bumi propagated by seed collected from Jambi using RAPD marker. Propagation by seed produced low germination percentage (14-34%) at different media. Seedling planted in pure carbonized rice husk medium produced the best growth variabel on vigority, primary root number, secondary root number, primary root length and secondary root length. Result from stem cutting showed that medium significantly improved secondary root length, while rooting percentage, primary root length and the number of root significantly was affected by Rootone F treatment. Genetic relatedness by RAPD marker showed that pasak bumi propagated by seed has high value of genetic diversity within population (He = 0,3076) and 78,57% all the loci tested were polimorphic, clustering analysis showed that the plant can be grouped into two group.
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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