Judul: Analisis Sistem Distribusi Air Bersih di Perumahan Ciomas Permai, Kabupaten Bogor, Jawa Barat.
Abstrak: Sistem distribusi air bersih sering bermasalah dalam hal kuantitas, tekanan, kontinuitas dan kualitas air. Penelitian ini bertujuan untuk menganalisis sistem distribusi air bersih PDAM Tirta Kahuripan, Kabupaten Bogor di Perumahan Ciomas Permai. Penelitian dilakukan dengan menggunakan data primer dan data sekunder. Analisis sistem distribusi air bersih dilakukan dengan menggunakan aplikasi EPANET 2.0. Perumahan Ciomas Permai termasuk ke dalam zona 6 PDAM Tirta Kahuripan. Berdasarkan hasil penelitian didapatkan bahwa kualitas air yang didistribusikan telah sesuai dengan standar yang berlaku dan kontinyu selama 24 jam walaupun terdapat perbedaan debit yang signifikan saat jam puncak. Berdasarkan pengukuran pada hari Minggu dan Senin besarnya debit minimum sebesar 14.4 l/det dan 13.8 l/det, melebihi kebutuhan pelanggan sebesar 7.34 l/det, sedangkan tekanan berkisar antara 0.7 – 1.35 bar. Pada simulasi distribusi air bersih menggunakan EPANET 2.0 didapatkan bahwa kecepatan air dan headloss berdasarkan simulasi tidak memenuhi persyaratan yang berlaku.
Keyword: debit, EPANET 2.0, headloss, kualitas air, tekanan

Judul: Analisis Sistem Distribusi Air Bersih Daerah Pelayanan Zona 6 PDAM Tirta Pakuan Bogor, Jawa Barat
Abstrak: Air bersih merupakan kebutuhan dasar bagi manusia sehingga sektor air bersih mendapat prioritas dalam penanganan dan pemenuhannya. PDAM sebagai perusahaan daerah pengelola air bersih seharusnya mampu untuk memenuhi kebutuhan tersebut. Tujuan penelitian ini adalah melakukan analisis kinerja sistem distribusi air bersih yang meliputi kualitas air, kuantitas (debit) dan kontinuitas, melakukan analisis kecukupan air bersih serta melakukan analisis hidrolika yang meliputi parameter tekanan, kecepatan dan headloss. Berdasarkan analisis yang dilakukan, kualitas air bersih di daerah pelayanan zona 6 telah memenuhi syarat baku mutu Permenkes No 492/Menkes/Per/IV/2010. Namun, pasokan air sering terhenti di daerah pelayanan yang disebabkan oleh kebocoran. Kebutuhan air di daerah pelayanan zona 6 sudah tercukupi, karena kebutuhan air sebesar 125,6 lt/dt sedangkan total produksi air sebesar 132,1 lt/dt. Berdasarkan analisis dengan software EPANET 2.0, nilai tekanan tertinggi terjadi pada node 8 sebesar 8,8 bar dan terendah pada node 12 sebesar 0,1 bar. Nilai headloss tertinggi sebesar 9,39m dan kecepatan tertinggi sebesar 1,37 m/dt terjadi pada pipa 1. Nilai headloss terendah sebesar 0,07 m dan kecepatan terendah 0,07 m/dt terjadi pada pipa 6.
Keyword: air bersih, EPANET 2.0, kebutuhan air, sistem distribusi

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