Judul: Pengembangan Kelembagaan Pesantren Sebagai Upaya Pengembangan Masyarakat (Studi Kasus Pondok Pesantren Miftahulhuda Al-Musri’ Desa Kertajaya Kecamatan Ciranjang Kabupaten Cianjur, Jawa Barat)
Abstrak: Peran pesantren selama ini dikenal terbatas pada lembaga pendidikan tradisional berbasis agama dengan kiai dan santri-santri sebagai komponen di dalamnya. Pesantren saat ini telah mengalami banyak kemajuan dalam berbagai bidang, tidak hanya lembaga pendidikan tradisional tetapi juga sebagai cikal bakal perubahan pada masyarakat. Oleh karena itu, penelitian ini penting sebagai media informasi terhadap pemerintah ataupun masyarakat luas bahwa pesantren memiliki peran dalam pembangunan. Penelitian ini bertujuan untuk mengetahui : (1) Bagaimana peran pesantren dalam pengembangan masyarakat? (2) Bagaimana profil komunitas Desa Kertajaya? (3) Bagaimana strategi dan bentuk yang dilakukan oleh pesantren dalam mengembangkan kelembagaannya dalam bidang ekonomi, sosial keagamaan dan pendidikan sebagai upaya pengembangan masyarakat? (4) Kendala apa saja yang dihadapi oleh pesantren dalam pengembangan kelembagaan tersebut dan (5) Bagaimana dampak pengembangan kelembagaan tersebut terhadap masyarakat?
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Judul: Peranan Pesantren dalam Pembangunan Pedesaan
Abstrak: Pesantren (pondok atau pondok pesantren) adalah suatu lembaga pendidikan keagamaan Islam yang pada umumnya tumbuh di kalangan masyarakat pedesaan. Pertumbuhannya merupakan hasil refleksi pimpinan pesantren dan masyarakat terhadap kebutuhan masyarakat sekitar. Disamping sebagai lembaga pendidikan keagamaan, diharapkan pesantren dapat berperan sebagai lembaga sosial kemasyarakatan yang dapat membantu pemerintah dalam menyebar luaskan inovasi pembangunan kepada masyarakat, dan menggerakkan masyarakat agar berperan serta dalam pembangunan.
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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