Judul: Hubungan Curah Hujan dan Titik Panas (Hotspot) dalam Kaitannya dengan Terjadinya Kebakaran di Provinsi Aceh
Abstrak: Kebakaran hutan dan lahan di Provinsi Aceh dari tahun ke tahun semakin meluas dan bertambah. Meskipun pada beberapa tahun sempat terjadi penurunan, pada tahun 2012 di Provinsi Aceh terjadi peningkatan jumlah kebakaran yang paling tinggi. Penelitian ini bertujuan untuk menganalisis hubungan antara curah hujan dengan titik panas (hotspot) di Provinsi Aceh terkait dengan terjadinya kebakaran hutan di Provinsi Aceh dan mengetahui wilayah yang paling parah dilanda kebakaran. Hasil penelitian ini menunjukkan bahwa musim kemarau di Provinsi Aceh terjadi pada bulan Mei sampai Oktober dengan puncak musim kemarau pada bulan Juni. Peningkatan jumlah hotspot ini mengikuti pola curah hujan yang rendah. Keadaan ini menjelaskan bahwa peningkatan dan penurunan jumlah hotspot di Provinsi Aceh berkaitan dengan penurunan dan peningkatan curah hujan di Provinsi Aceh. Penelitian ini menunjukkan bahwa daerah di Provinsi Aceh yang mengalami kebakaran hutan terparah pada periode 2008-2013 dengan jumlah hotspot tertinggi terdeteksi pada Kabupaten Aceh Barat (969 hotspot), Kabupaten Naganraya (840 hotspot), dan Kabupaten Aceh Singkil (687 hotspot).
Keyword: Curah hujan, hotspot, kebakaran hutan, Provinsi Aceh

Judul: Pola Sebaran Titik Panas (Hotspot) Sebagai Indikator Terjadinya Kebakaran Hutan dan Lahan di Kabupaten Aceh Barat
Abstrak: Kabupaten Aceh Barat merupakan salah satu kabupaten yang sering terjadi kebakaran hutan dan lahan. Perlu adanya melakukan pengendalian kebakaran hutan dan lahan, salah satunya yaitu pencegahan. Pencegahan kebakaran hutan dan lahan dapat memanfaatkan data titik panas untuk dianalisis dengan menggunakan Sistem Informasi Geografis (SIG). Penelitian ini bertujuan menganalisis sebaran titik panas dan hubungan curah hujan dengan titik panas sebagai indikator terjadinya kebakaran hutan dan lahan di Kabupaten Aceh Barat pada tahun 2014-2019. Penelitian ini menggunakan data titik panas NASA MODIS, peta sebaran penutupan lahan, peta sebaran lahan gambut, peta administrasi dan data curah hujan dari BMKG. Hasil penelitian ditemukan sebanyak 576 titik panas di Kabupaten Aceh Barat dari tahun 2014-2019. Kecamatan dengan jumlah titik panas terbanyak berada di Kecamatan Samatiga yaitu sebanyak 131 titik panas. Titik panas paling mendominasi di tutupan lahan gambut sebanyak 64% dan daerah penutupan lahan belukar rawa sebanyak 126 titik panas. Hasil uji korelasi menunjukkan curah hujan dengan titik panas memiliki korelasi dengan arah korelasi negatif, bahwa penurunan curah hujan diikuti dengan kenaikan titik panas., Aceh Barat District is one of the districts where forest and land fires often occur. It is necessary to control forest and land fires, one of which is prevention. Forest and land fires prevention can be done by utilizing hotspot data for analysis using geographic information systems (GIS). This research aims to analyze the distribution of hotspots and the correlation between rainfall and hotspots as an indicator of the occurrence of forest and land fires in West Aceh Regency in 2014-2019. This research uses NASA MODIS hotspots, land cover distribution maps, peat land distribution maps, administrative maps and rainfall data from BMKG. The resuls of the research found that there were 576 hotspots in West Aceh Regency from 2014-2019. The district with the highest number of hotspots is in Samatiga District, namely 131 hotspots. The most dominant hotspots are in the peatland cover, as much as 64% and in the swamp scrub land cover area with 126 hotspots. Correlation test results show that rainfall with a negative correlation, that the decrease in rainfall is followed by an increase in hotspots.
Keyword: Aceh Barat, Curah hujan, lahan gambut, penutupan lahan, titik panas

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