Judul: Penentuan Karakteristik Akifer dan Potensi Airbumi di Jakarta
Abstrak: Groundwater is one of the water resources used for domestic and industrial water uses, particularly in Jakarta region. Excessive extraction of groundwater has caused groundwater depletion and land subsidance. This study aimed to determine the characteristics of aquifer and groundwater potential of the Jakarta region based on available geologic logs and well data, including pumping test data. Analysis of geological log indicated that Jakarta region had several layers of confined aquifer namely aquifer 20 – 30 m below ground and another aquifer 50 – 170 m below the ground surface. Analysis result of the pumping test data from 14 production wells in Jakarta region indicated transmisivity value ranged from 5 to 522.8 m2/days, while the values of hydraulic conductivity of the aquifer system in Jakarta region ranged from 0.62 to 58.09 m/day. Hydraulic conductivity values indicated that the rock types of aquifer in Jakarta region were dominated by fine sands and clay. From the aquifer characteristic, potential groundwater in Jakarta region ranged from 5 to 522.8 m3/day/ meter aquifer. Groundwater potential of each well in Jakarta region was still not fully utilized due to improper pumping construction in positioning the well –screen-, where was not installed properly on aquifer layers but on clay layers, so the well efficiency become low with the consequences of high operation costs.
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Judul: Kajian Potensi dan Supply-Demand Airbumi di Kecamatan Citeureup, Kabupaten Bogor
Abstrak: Human life creature else cannot life without groundwater. In Citeureup subdistrict, groundwater utilization for industry and housekeepinGunung Groundwater utilization need be increasinGunung Whereas groundwater availability be limited by nature condition in this area. Highly productive aquifer in Citeureup subdistrict is obtained from the alluvium river deposits, mainly a long both sides of Citeureup rivers, Cileungsi rivers, and Cijere riverSungai Well yield ranges between 2 and 5 l/sec in sand and gravel deposits with intergranular groundwater flow. Good quality of groundwater still found both in shallow and depth of aquifer. Based on quantity and quality of groundwater, the management of supply demand balance must be done. This study to give description about availability and demand of groundwater for supporting activity in Citeureup subdistrict.
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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