Judul: Pola Konsumsi, Pengeluaran dan Willingness to Pay Rumah Tangga terhadap Layanan Air Bersih
Abstrak: Pencemaran air tanah dan kelangkaan akses sumber air bersih merupakan masalah utama di beberapa daerah di Indonesia, salah satunya di Kelurahan Kamal, Kecamatan Kalideres, Jakarta Barat. Tujuan penelitian ini adalah membandingkan pola konsumsi dan pengeluaran rumah tangga antara rumah tangga yang telah memiliki jaringan air perpipaan dengan rumah tangga yang belum memiliki jaringan air perpipaan. Identifikasi sumber air dan estimasi volume pemakaian air berdasarkan pendapatan pada masing-masing sumber dianalisis menggunakan tabulasi dan analisis deskriptif, perbandingan pengeluaran konsumsi air dianalisis menggunakan analisis pendapatan, estimasi nilai keinginan masyarakat atas jaringan air perpipaan PT. Palyja dianalisis menggunakan analisis Willingness To Pay (WTP), serta estimasi surplus konsumen dianalisis menggunakan analisis surplus konsumen. Berdasarkan hasil keempat analisis tersebut, dapat disimpulkan bahwa secara nominal pengeluaran konsumsi air rumah tangga yang belum memiliki jaringan air perpipaan lebih rendah daripada rumah tangga yang telah memiliki jaringan air perpipaan, namun karena pendapatan rumah tangga yang belum memiliki jaringan air perpipaan lebih rendah, maka proporsi pengeluaran konsumsi air mereka menjadi lebih tinggi. Nilai WTP yang diperoleh lebih besar daripada harga yang sebenarnya konsumen bayarkan jika mendapat jaringan air perpipaan, maka masyarakat mendapatkan surplus konsumen.
Keyword: analisis pendapatan, layanan air bersih, surplus konsumen, willingness to pay.

Judul: The Pattern of Household Consumption and Expenditure for Clean Water in Kampung Luar Batang, North Jakarta
Abstrak: Kelangkaan air bersih di Kampung Luar Batang mengakibatkan masyarakat harus memenuhi kebutuhan airnya dari berbagai sumber, sehingga menyebabkan peningkatan biaya untuk mendapatkan air. Penelitian ini bertujuan untuk mengidentifikasi pola konsumsi air bersih berdasarkan sumber-sumber air bersih, menganalisis persepsi rumah tangga terhadap air bersih, menganalisis faktor-faktor yang memengaruhi konsumsi air bersih, dan membandingkan pengeluaran untuk konsumsi air bersih terhadap total pendapatan rumah tangga. Penelitian ini menggunakan metode analisis deskriptif, skala likert, regresi linear berganda, dan analisis proporsi pengeluaran. Hasil penelitian menunjukkan (1) Rumah tangga menggunakan empat sumber air bersih; (2) Persepsi rumah tangga menunjukkan bahwa berdasarkan kategori pelayanan, kualitas, dan sikap pedagang air bersih, air minum dalam kemasan mendapatkan skor tertinggi dibandingkan sumber air bersih lain; (3) Terdapat tiga faktor yang memengaruhi konsumsi air bersih di Kampung Luar Batang, yaitu jumlah anggota keluarga, pendapatan rumah tangga, dan luas bangunan rumah; (4) Rumah tangga yang tidak mengalami kelangkaan air bersih lebih hemat dalam pengeluaran untuk konsumsi air., Scarcity of clean water in Kampung Luar Batang has resulted in the community having to meet their water needs from other sources, which has led to an increase in the cost of obtaining water. This study aims to identify patterns of clean water consumption based on clean water sources, analyze household perceptions of clean water, analyze factors that influence clean water consumption, and compare expenditures for clean water consumption to total household income. This research uses descriptive analysis method, likert scale, multiple linear regression, and expenditure proportion analysis. The results showed (1) Households use four sources of clean water; (2) Household perceptions indicate that based on the category, quality, and attitude of clean water traders, bottled drinking water gets the highest score compared to other source of clean water; (3) There are three factors that influence the consumption of clean water in Kampung Luar Batang, namely number of family members, household income, and the area of house building; (4) Households that do not experience a scarcity of clean water are more efficient in spending on water consumption.
Keyword: cost, multiple linear regression, volume, perception, price

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