Judul: Studi Kasus di Pasar Induk Kramat Jati DKI Jakarta
Abstrak: Peran komoditas cabai yang cukup penting dan penggunaannya yang luas membuat cabai merah memiliki nilai ekonomis yang cukup baik. Meskipun demikian, komoditas ini mempunyai masalah fluktuasi harga yang cukup besar. Harga cabai dapat berfluktuasi setiap harinya, bahkan setiap jam. Misalkan siang hari harga tinggi namun di sore hari harga bisa saja jatuh. Ini merupakan fenomena yang terjadi di pasar.
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Judul: Analisis pemasaran cabai merah besar (Capsicum annuum var.longum) di DKI Jakarta: Kasus di Pasar Induk Kramat Jati, Pasar Jatinegara, dan Pasar Tanah Abang DKI Jakarta
Abstrak: Cabai sebagai salah satu komoditas hortikultura untuk jenis sayuran, memiliki manfaat yang besar dan dibutuhkan oleh hampir semua golongan masyarakat. Permintaan konsumen terhadap komoditas ini cenderung terus meningkat dari tahun ke tahun. Pada tahun 1990 konsumsi cabai oleh masyarakat Indonesia sebesar 513.130 ton. Tahun 1995, konsumsi cabai sudah mencapai 1.069.500 ton. Pada periode Januari hingga September 1996 konsumsi cabai mencapai 915.980 ton. Permintaan terhadap cabai masih dapat diimbangi oleh produksi cabai setiap tahunnya. Tahun 1990, produksi cabai Indonesia barn sebesar 569.604 ton. Pada tahun 1995 produksi cabai sudah mencapai 1.589.977 ton, dan periode Januari - September 1996 mencapai 1.013.746 ton. Meskipun jumlah produksi masih dapat memenuhi permintaan cabai, sering terjadi ketidakseimbangan antara permintaan dan penawaran cabai. Akibatnya harga cabai di pasar tidak stabil. Distribusi cabai yang melibatkan lembaga pemasaran sangat mempengaruhi kestabilan harga dan efisiensi pemasaran cabai dari daerah produsen ke daerah konsumsi seperti DKI Jakarta. Oleh karena itu perlu ditelaah sampai sejauh mana efisiensi pemasaran cabai di daerah konsumsi DKI Jakarta.
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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