Judul: Studi makrozoobenthos dan habitatnya di perairan pelabuhan tanjung priok dan perairan sekitarnya
Abstrak: Tujuan penelitian ini untuk mendeskripsikan jenis makrozoobenthos yang hidup di perairan Pelabuhan Tanjung Priok dan di perairan sekitarnya, mengkaji hubungan antara komunitas makrozoobenthos dan habitat sebagai tempt hidupnya di perairan Pelabuhan Tanjung Priok dan di perairan sekitarnya (Muara Gembong dan Tanjung Karawang) dan mengkaji pengaruh antara musim kemarau dan musim peralihan terhadap kepadatan makrozoobenthos.
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Judul: Ekotipe komunitas makrozoobenthos pada perairan sungai di Sumatera Selatan dan Lampung
Abstrak: Ekosistem perairan sungai dan laut digolongkan sebagai perairan dengan sistem terbuka (open water system), yang berarti sangat dipengaruhi oleh keadaan lingkungan sekitarnya. Kedua ekosistem ini memiliki keterkaitan yang erat dimana laut merupakan tempat bermuaranya sungai-sungai. Tipe-tipe organisme yang hidup di ekosistem perairan memiliki karakteristik yang berbeda-beda sesuai dengan karakteristik dan jenis perairannya. Organisme benthos adalah organisme yang tinggal di dalam dan/atau di atas sedimen dasar perairan, yang memiliki siklus hidup yang panjang dan pergerakkan yang terbatas (Lind 1979 dalam Suryadiputra, 1993). Peranan benthos meliputi kemampuannya dalam mendaur ulang bahan-bahan organik, membantu proses mineralisasi dan kedudukannya dalam beberapa posisi penting dalam rantai makanan, sehingga dapat dipakai untuk menduga kesuburan perairan. Benthos dipakai sebagai indikator pencemaran, mengingat sifatnya yang menetap dan tidak dapat menghindar dalam kontak dengan air limbah atau bahan pencemar. Penelitian ini dilakukan di Sumatera Selatan dan Lampung yang merupakan kawasan yang potensial bagi pengembangan ekonomi dan industri sehubungan dengan ketersediaan sarana dan prasarana yang terus meningkat. Penelitian ini bertujuan untuk mengetahui struktur dan organisme komunitas makrozoobenthos, Kondisi kualitas perairan dan keterkaitannya dengan struktur komunitas makrozoobenthos pada perairan Sungai di Sumatera Selatan dan Lampung.
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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