Judul: Tipologi Komunitas Makrozoobenthos di Sungai Cigudeg pada Lokasi Sekitar Pembuangan Limbah Cair Terolah P.T Unitex Bogor, Jawa Barat
Abstrak: Sungai Cigudeg (Sungai Cigudig), merupakan salah satu anak Sungai Ciliwung yang terletak di depan pabrik tekstil P.T Unitex. Selain digunakan untuk keperluan rumah tangga oleh penduduk di sekitarnya sungai ini digunakan pula oleh pabrik ini sebagai tempat pembuangan Iimbah cair yang telah diolah. Tujuan dari peneiitian ini ada untuk mendeterminasi tipologi komunitas makrozoobenthos di Sungai Cigudeg, digunakan sebagai ternpat pembuangan limbah cair terolah dari pabrik tekstil P.T % : % 2 :ex, Bogor.
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Judul: Struktur komunitas makrozoobenthos sebagai indikator kualitas lingkungan perairan Sungai Cigede, Bukit Sentul, Bogor
Abstrak: Ruas bagian hulu Sungai Cigede melintasi rencana kawasan perumahan Bukit Sentul, Bogor dan pada saat penelitian ini dilakukan tengah berlangsung kegiatan pembangunan perumahan secara besar-besaran di dalam kawasan tersebut. Di masa mendatang hal ini diduga dapat menimbulkan masalah, sebab limbah buangan yang berasal dari perumahan akan masuk ke dalam sungai sehingga dapat menyebabkan perubahan kualitas perairan. Salah satu organisme akuatik yang akan merasakan langsung pengaruh tersebut adalah makrozoobenthos, sebab pada umumnya organisme ini bersifat menetap atau relatif tidak bisa berpindah tempat bila terjadi perubahan di dalam lingkungannya. Penelitian ini bertujuan untuk memberikan infonnasi dasar mengenai kualitas perairan Sungai Cigede berdasarkan struktur komunitas makrozoobenthos sebagai aspek utama dan parameter fisika kimia sebagai aspek penunjang. Penelitian dilakukan pada bulan Agustus 1998 (2 kali pengamatan) di Sungai Cigede, Bukit Sentul, Bogor. Pengambilan contoh pada 5 stasiun ditentukan berdasarkan perbedaan kondisi tata guna lahan di sekitar daerah aliran Sungai Cigede. Parameter yang diukur meliputi parameter fisika (suhu, debit substrat kekeruhan, OHL, TS), kimia (pH, DO, B0D₅, alkalinitas, kesadahan, nitrat, fosfat) dan biologi (makrozoobenthos).
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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