Judul: Status Ekologi dan Status Kesuburan Danau Hias Crown Golf, Pantai Indah Kapuk, Jakarta Utara.
Abstrak: Danau Hias Crown Golf merupakan salah satu perairan menggenang buatan yang terletak di Pantai Indah Kapuk, Jakarta Utara. Tingginya bahan organik yang masuk ke perairan ini dapat mengubah kualitas air, meningkatkan kesuburan, serta mempengaruhi kondisi ekologi perairan. Tujuan dari penelitian ini adalah menganalisis status ekologi dan status kesuburan perairan Danau Hias Crown Golf berdasarkan keberadaan fitoplankton. Status kesuburan perairan dianalisis dengan menggunakan Indeks Nygaard dan Indeks Thunmark, sedangkan status ekologi dianalisis dengan Indeks Q. Fitoplankton yang memiliki kelimpahan tertinggi di Danau Hias Crown Golf adalah kelas Bacillariophyceae. Komposisi kelimpahan fitoplankton pada Stasiun 1 sampai 4 didominasi oleh kelas Bacillariophyceae dengan persentase pada masing-masing stasiun pengamatan sebesar 50,74%, 67,96%, 35,03%, dan 81,70%. Hasil penelitian menunjukkan nilai Indeks Nygaard sebesar 9,5-10, Indeks Thunmark sebesar 4- 4,5, dan Indeks Q sebesar 0,92-2,87. Secara keseluruhan dapat disimpulkan bahwa tingkat kesuburan perairan Danau Hias Crown Golf adalah eutrof, dengan status ekologi yang sedang hingga sangat buruk.
Keyword: fitoplankton, kualitas air, status ekologi, tingkat kesuburan

Judul: Tingkat Kesuburan dan Status Ekologi Danau Hias Garden House, Pantai Indah Kapuk, Jakarta Utara
Abstrak: Danau Hias Garden House merupakan salah satu perairan menggenang buatan yang terletak di Pantai Indah Kapuk dengan kedalaman kurang dari 1 meter dan mendapat banyak masukan bahan organik dari aktivitas domestik. Bahan organik yang masuk dapat mengubah kualitas air, meningkatkan kesuburan, serta mempengaruhi kondisi ekologi perairan. Tujuan dari penelitian ini adalah menganalisis tingkat kesuburan dan status ekologi perairan Danau Hias Garden House. Tingkat kesuburan perairan dianalisis dengan menggunakan Indeks Nygaard, sedangkan status ekologi dianalisis dengan Indeks Q dan MedPTI. Cyclotella sp. merupakan jenis fitoplankton yang memiliki kelimpahan tertinggi di Danau Hias Garden House. Konsentrasi P total di Danau Hias Garden House sangat tinggi melebihi 0,1 mg/L. Hasil penelitian menunjukkan nilai Indeks Nygaard sebesar 9,5-10,5, Indeks Q 1,41-1,57, dan Indeks MedPTI 1,46-1,85. Secara keseluruhan dapat disimpulkan bahwa tingkat kesuburan perairan Danau Hias Garden House adalah eutrof dengan status ekologi buruk sampai sangat buruk.
Keyword: kualitas air, status ekologi, tingkat kesuburan

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