Judul: Analisis kesukaan habitat ikan karang di sekitar Pulau Batam, Kepulauan Riau
Abstrak: Indonesia sebagai negara kepulauan yang secara geografis terletak di antara Samudera Pasifik dan Samudera Hindia memiliki kekayaan keanekaragaman hayati baik di darat maupun di laut. Sebagai negara tropis, Indonesia memiliki potensi sumberdaya perairan yang cukup besar. Salah satu sumberdaya alam perairan tropis yang penting dan memiliki potensi yang besar adalah kawasan terumbu karang. Terumbu karang memiliki nilai dan arti yang sangat penting baik dari segi ekologi laut maupun sosial ekonomi. Ditinjau dari segi ekologi laut, terumbu karang memiliki fungsi antara lain sebagai gudang keanekaragaman hayati, tempat tinggal sementara atau tetap, tempat mencari makan, berpijah, daerah asuhan dan tempat berlangsungnya siklus biologi, kimia, fisika secara global yang memiliki tingkat produktivitas yang sangat tinggi dan juga sebagai pelindung dari hempasan gelombang (Suharsono, 1996). Dari segi sosial ekonomi, terumbu karang memiliki nilai ekonomi yang sangat tinggi. Nilai perikanan karang di Asia Tenggara mencapai 2,4 milyar dollar AS/thn.
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Judul: Analisis ekonomi terumbu karang (Studi kasus di Kawasan Kelurahan Pulau Kelapa, Taman Nasional Laut Kepulauan Seribu, DKI Jakarta.)
Abstrak: Salah satu biota laut yang sangat bermanfaat bagi kelangsungan hidup biota laut lainnya adalah terumbu karang. Terumbu karang merupakan sumber mata pencaharian utama bagi ratusan hingga ribuan nelayan terutama pada waktu paceklik. Terumbu karang juga berfungsi sebagai penahan terhadap erosi gelombang laut, sehingga melindungi pantai dan kawasan pemukiman pantai, lahan pertanian dan pulau - pulau kecil. Terumbu karang merupakan sumber devisa yang diperoleh dari para pengelola wisata bahari.
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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