Judul: Keanekaragaman serangga penyerbuk dan efektivitasnya dalam pembentukan buah pala (Myristica fragrans Houtt: Myristiceae)
Abstrak: Pala Banda (Myristica fragrans Houtt) merupakan tanaman asli Indonesia yang berasal dari kepulauan Banda dan Maluku. Tanaman pala banyak ditanam di daerah-daerah yang mempunyai ketinggian 500 - 700 m di atas permukaan laut. Bagian tanaman pala yang dimanfaatkan antara lain biji, fuli, dan buah. Pala merupakan tanaman tahunan dan sebagian besar berumah dua (unisex dioecius).
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Judul: Inventarisasi Serangga Pengganggu Dan Penyakit Tanaman Pala (Myristica fragrans Houtt) Di Kecamatan Cibeber, Kabupaten Cianujur Propinsi Jawa Barat
Abstrak: Pala (Myristica fragrans Houtt.) termasuk tanaman rempah-rempah yang sudah dikenal sejak beberapa abad yang lalu. Sebagai tanaman rempah-rempah, pala penting artinya karena dapat memberikan aroma terhadap berbagai makanan, sehingga dapat menstimulir nafsu makan. Fuli dan biji pala banyak digunakan dalam industri pembuatan sosis. Fuli dapat pula digunakan sebagai bahan mentah dalam industri pengawetan ikan dan sebagai adonan pembuatan kue. Daging buah pala dapat dijadikan manisan basah atau kering. Minyak pala yang diperoleh dari perasan biji pala dengan suhu tinggi, digunakan dalam industri obat-obatan, pembuatan sabun, minyak rambut dan parfum (Andrew, 1965). Sampai tahun 1982, Indonesia merupakan negara penghasil dan pengekspor pala terbesar di dunia (Tabel 1). Daerah sentra tanaman pala di Indonesia adalah Aceh, Sumatera Barat, Sulawesi Utara, Maluku dan Irian Jaya (Anonim, 1984). Fuli dan biji pala dari Sulawesi Utara dan Maluku banyak dipasarkan ke luar negeri sebagai penghasil devisa negara, Di Indonesia, tanaman pala diusahakan oleh perkebunan rakyat, perkebunan besar swasta dan perkebunan besar negara (Anonim, 1984). Pada tahun 1983, luas areal pertanaman pala yang diusahakan perkebunan rakyat adalah seluas 59 579 hektar atau 94.16 persen yang tersebar di Indonesia; perkebunan besar swasta seluas 1 991 hektar atau 3.15 persen di daerah Aceh, Jawa Tengah, Maluku dan Irian Jaya; perkebunan besar negara seluas 1 700 hektar atau 2.69 persen di daerah Jawa Tengah dan Jawa Timur (Anonim, 1984).
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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