Judul: Keanekaragaman Spesies Tumbuhan Aromatik di Kebun Raya Bogor
Abstrak: Indonesia merupakan salah satu negara penghasil tumbuhan aromatik yang cukup penting di dunia. Potensi tumbuhan aromatik harus terus dijaga dan dilestarikan. Tujuan penelitian ini adalah untuk mengidentifikasi spesies tumbuhan aromatik di Kebun Raya Bogor (KRB), mengidentifikasi spesies yang potensial sebagai tumbuhan penghasil minyak atsiri di KRB, menentukan status konservasi tumbuhan aromatik di KRB, dan mengidentifikasi pengetahuan pengunjung mengenai tumbuhan aromatik di KRB. Penelitian dilakukan dengan metode studi pustaka, inventarisasi potensi, uji fitokimia, dan wawancara. Hasil penelitian menunjukkan bahwa tumbuhan aromatik di Kebun Raya Bogor teridentifikasi sebanyak 132 spesies dengan spesies tumbuhan terbanyak dari famili Zingiberaceae (14.39%). Habitus tumbuhan didominasi oleh pohon (56.06%), dan bagian yang paling banyak mengandung minyak atsiri adalah daun (28.37%). Uji fitokimia menunjukkan terdapat 15 spesies yang berpotensi sebagai tumbuhan penghasil minyak atsiri. Hasil wawancara menunjukkan bahwa 69% pengunjung KRB memiliki pengetahuan tentang tumbuhan aromatik.
Keyword: keanaekaragaman, konservasi ex-situ, KRB, tumbuhan aromatik

Judul: Keanekaragaman dan Potensi Spesies Tumbuhan Bawah pada Beberapa Tegakan Famili Pohon di Kebun Raya Bogor.
Abstrak: Kebun Raya adalah kawasan konservasi tumbuhan secara ex-situ dan terdapat sistem pendokumentasian pada koleksi tumbuhannya. Salah satu kebun raya yang ada di Indonesia yaitu Kebun Raya Bogor (KRB). Koleksi tumbuhan yang ada di KRB terdiri dari berbagai spesies dan habitus, diantaranya yaitu tumbuhan bawah. Penelitian ini bertujuan untuk mengidentifikasi keanekaragaman dan potensi spesies tumbuhan bawah, serta mendeskripsikan kondisi faktor lingkungan abiotik pada beberapa tegakan pohon di KRB. Metode pengambilan data dilakukan dengan analisis vegetasi, observasi lapang, dan studi literatur. Hasil penelitian menunjukkan bahwa teridentifikasi 37 spesies tumbuhan bawah dari 20 famili. Tumbuhan bawah yang diperoleh dari hasil analisis vegetasi berpotensi sebagai tumbuhan obat, tanaman hias, bioherbisida, dan pembersih udara. Kondisi lingkungan abiotik yang diukur pada plot penelitian menunjukkan nilai yang relatif sama kecuali pada nilai intensitas cahaya matahari.
Keyword: keanekaragaman, kebun raya bogor, tumbuhan bawah

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