Judul: Analisis investasi pengembangan pengelolaan fasilitas rekreasi di Taman Wisata Alam Gunung Tangkuban Parahu Propinsi Jawa Barat
Abstrak: Kayu memiliki sifat yang menguntungkan dan kurang menguntungkan. Salah satu sifat kayu yang kurang menguntungkan adalah kepekaannya terhadap organisma perusak kayu seperti jamur, serangga, dan binatang laut. Pengawetan adalah salah satu usaha untuk mengatasi hal tersebut. Dengan pengawetan maka umur pakai kayu dapat ditingkatkan. Penggunaan NAOH (Natrium Hidroksida) dalam perlakuan terhadap kayu dapat dijadikan alternatif bahan pengawet karena menyebabkan kayu menjadi tidak disenangi oleh faktor perusak.
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Judul: Analisis investasi pengembangan pengelolaan fisik rekreasi di Wana Wisata Watu Ulo Jember Jawa Timur
Abstrak: Peningkatan kesadaran manusia akan pentingnya menjaga lingkungan yang disertai oleh peningkatan pendapatan per- kapita secara kontinyu akan menggeser pola konsumsi ke arah konsumsi jasa rekreasi, pendidikan dan penelitian, khususnya yang disediakan oleh ekosistem hutan. Menurut Darusman (1987) salah satu upaya untuk mengembangkan man- faat intangible sumberdaya hutan, adalah dengan mengem- bangkan Rekreasi alam. P Untuk mengembangkan potensi rekreasi alam tersebut, tentu diperlukan input baik modal maupun tenaga kerja. Oleh karena itu, perlu dilakukan suatu penilaian yang obyektif secara kuantitatif terhadap besarnya input yang harus diberikan dan manfaat yang diperoleh, sehingga dapat dicapai pengelolaan yang efisien dengan hasil yang opti- mum. Sebagai salah satu alternatif tempat rekreasi alam yang menyehatkan dan mengandung unsur pendidikan, Wana Wisata Watu Ulo merupakan salah satu wujud dari upaya pemasaran manfaat intangible. Pengelolaan dan pengem- bangan Wana Wisata Watu Ulo yang sehat dan dinamis akan memberikan manfaat yang penting bagi pemerintah dan masya- rakat. Suatu analisis investasi yang dapat menggambarkan...
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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