{"title":"Random plane increasing trees: Asymptotic enumeration of vertices by distance from leaves","authors":"M. Bóna, B. Pittel","doi":"10.1002/rsa.21138","DOIUrl":"https://doi.org/10.1002/rsa.21138","url":null,"abstract":"We prove that for any fixed k$$ k $$ , the probability that a random vertex of a random increasing plane tree is of rank k$$ k $$ , that is, the probability that a random vertex is at distance k$$ k $$ from the leaves, converges to a constant ck$$ {c}_k $$ as the size n$$ n $$ of the tree goes to infinity. We prove that 1−∑j≤kck<22k+3(2k+4)!$$ 1-{sum}_{jle k}{c}_k<frac{2^{2k+3}}{left(2k+4right)!} $$ , so that the tail of the limiting rank distribution is super‐exponentially narrow. We prove that the latter property holds uniformly for all finite n$$ n $$ as well. More generally, we prove that the ranks of a finite uniformly random set of vertices are asymptotically independent, each with distribution {ck}$$ left{{c}_kright} $$ . We compute the exact value of ck$$ {c}_k $$ for 0≤k≤3$$ 0le kle 3 $$ , demonstrating that the limiting expected fraction of vertices with rank ≤3$$ le 3 $$ is 0.9997$$ 0.9997 $$ … We show that with probability 1−n−0.99ε$$ 1-{n}^{-0.99varepsilon } $$ the highest rank of a vertex in the tree is sandwiched between (1−ε)logn/loglogn$$ left(1-varepsilon right)log n/mathrm{loglog}n $$ and (1.5+ε)logn/loglogn$$ left(1.5+varepsilon right)log n/mathrm{loglog}n $$ , and that this rank is asymptotic to logn/loglogn$$ log n/mathrm{loglog}n $$ with probability 1−o(1)$$ 1-o(1) $$ .","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"2013 1","pages":"102 - 129"},"PeriodicalIF":1.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86321615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"1‐independent percolation on ℤ2×Kn","authors":"Victor Falgas‐Ravry, Vincent Pfenninger","doi":"10.1002/rsa.21129","DOIUrl":"https://doi.org/10.1002/rsa.21129","url":null,"abstract":"A random graph model on a host graph H$$ H $$ is said to be 1‐independent if for every pair of vertex‐disjoint subsets A,B$$ A,B $$ of E(H)$$ E(H) $$ , the state of edges (absent or present) in A$$ A $$ is independent of the state of edges in B$$ B $$ . For an infinite connected graph H$$ H $$ , the 1‐independent critical percolation probability p1,c(H)$$ {p}_{1,c}(H) $$ is the infimum of the p∈[0,1]$$ pin left[0,1right] $$ such that every 1‐independent random graph model on H$$ H $$ in which each edge is present with probability at least p$$ p $$ almost surely contains an infinite connected component. Balister and Bollobás observed in 2012 that p1,c(ℤd)$$ {p}_{1,c}left({mathbb{Z}}^dright) $$ tends to a limit in [12,1]$$ left[frac{1}{2},1right] $$ as d→∞$$ dto infty $$ , and they asked for the value of this limit. We make progress on a related problem by showing that limn→∞p1,c(ℤ2×Kn)=4−23=0.5358….$$ underset{nto infty }{lim }{p}_{1,c}left({mathbb{Z}}^2times {K}_nright)=4-2sqrt{3}=0.5358dots . $$In fact, we show that the equality above remains true if the sequence of complete graphs Kn$$ {K}_n $$ is replaced by a sequence of weakly pseudorandom graphs on n$$ n $$ vertices with average degree ω(logn)$$ omega left(log nright) $$ . We conjecture the answer to Balister and Bollobás's question is also 4−23$$ 4-2sqrt{3} $$ .","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"104 1","pages":"887 - 910"},"PeriodicalIF":1.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80473334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Iterated tour partitioning for Euclidean capacitated vehicle routing","authors":"Claire Mathieu, Hang Zhou","doi":"10.1002/rsa.21130","DOIUrl":"https://doi.org/10.1002/rsa.21130","url":null,"abstract":"We give a probabilistic analysis of the unit‐demand Euclidean capacitated vehicle routing problem in the random setting. The objective is to visit all customers using a set of routes of minimum total length, such that each route visits at most k$$ k $$ customers. The best known polynomial‐time approximation is the iterated tour partitioning (ITP) algorithm, introduced in 1985 by Haimovich and Rinnooy Kan. They showed that the solution obtained by the ITP algorithm is arbitrarily close to the optimum when k$$ k $$ is either o(n)$$ oleft(sqrt{n}right) $$ or ω(n)$$ omega left(sqrt{n}right) $$ , and they asked whether the ITP algorithm was “also effective in the intermediate range”. In this work, we show that the ITP algorithm is at best a (1+c0)$$ left(1+{c}_0right) $$ ‐approximation, for some positive constant c0$$ {c}_0 $$ , and is at worst a 1.915‐approximation.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"93 1","pages":"1056 - 1075"},"PeriodicalIF":1.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82991010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Perfect sampling from spatial mixing.","authors":"Weiming Feng, Heng Guo, Yitong Yin","doi":"10.1002/rsa.21079","DOIUrl":"10.1002/rsa.21079","url":null,"abstract":"<p><p>We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with subexponential neighborhood growth like <math> <mrow> <msup><mrow><mi>ℤ</mi></mrow> <mrow><mi>d</mi></mrow> </msup> </mrow> </math> , our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer-dimer models in such graphs.</p>","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"61 4","pages":"678-709"},"PeriodicalIF":0.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ftp.ncbi.nlm.nih.gov/pub/pmc/oa_pdf/c0/27/RSA-61-678.PMC9790483.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10460725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mobile Commerce untuk Sales Order dan Tracking Order berbasis MVC","authors":"Andi Leo, Verri Kuswanto, Lily Damayanti","doi":"10.31253/algor.v4i1.1748","DOIUrl":"https://doi.org/10.31253/algor.v4i1.1748","url":null,"abstract":"Internet has become one of the important needs in everyday life. Internet access is very easy with various types of devices, one of which is mobile. This opens up opportunities for business people to serve customers in carrying out mobile-based transactions or what is called m-commerce. M-Commerce provides new innovations in the business world with the convenience it offers, making it used for new business breakthroughs, one of which is delivery service as a service that pampers buyers so they don't have to wait for goods or services ordered for days. This M-Commerce application for purchasing products or ordering services is built using the angularJS method based on the Model View Controller (MVC). This makes the software development cycle more streamlined and easy. This application provides easy service to m-commerce users because of the addition of delivery service, it is also expected to increase the purchase of goods or services on a regular basis. The conveniences obtained from this application are in the form of ordering goods which will then be delivered by the courier, tracking the courier's position while in the process of ordering, selecting products and services that are easier for users to see and viewing transactions and user history, on a mobile basis.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90263680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Conlon, J. Fox, Xiaoyu He, D. Mubayi, Andrew Suk, Jacques Verstraëte
{"title":"Hypergraph Ramsey numbers of cliques versus stars","authors":"D. Conlon, J. Fox, Xiaoyu He, D. Mubayi, Andrew Suk, Jacques Verstraëte","doi":"10.1002/rsa.21155","DOIUrl":"https://doi.org/10.1002/rsa.21155","url":null,"abstract":"Let Km(3)$$ {K}_m^{(3)} $$ denote the complete 3‐uniform hypergraph on m$$ m $$ vertices and Sn(3)$$ {S}_n^{(3)} $$ the 3‐uniform hypergraph on n+1$$ n+1 $$ vertices consisting of all n2$$ left(genfrac{}{}{0ex}{}{n}{2}right) $$ edges incident to a given vertex. Whereas many hypergraph Ramsey numbers grow either at most polynomially or at least exponentially, we show that the off‐diagonal Ramsey number r(K4(3),Sn(3))$$ rleft({K}_4^{(3)},{S}_n^{(3)}right) $$ exhibits an unusual intermediate growth rate, namely, 2clog2n≤r(K4(3),Sn(3))≤2c′n2/3logn,$$ {2}^{clog^2n}le rleft({K}_4^{(3)},{S}_n^{(3)}right)le {2}^{c^{prime }{n}^{2/3}log n}, $$for some positive constants c$$ c $$ and c′$$ {c}^{prime } $$ . The proof of these bounds brings in a novel Ramsey problem on grid graphs which may be of independent interest: what is the minimum N$$ N $$ such that any 2‐edge‐coloring of the Cartesian product KN□KN$$ {K}_Nsquare {K}_N $$ contains either a red rectangle or a blue Kn$$ {K}_n $$ ?","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"113 1","pages":"610 - 623"},"PeriodicalIF":1.0,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80640864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sistem Informasi Perkembangan Desa Sridadi Kec. Wonosoboh Kab. Tanggamus","authors":"Satria Abadi, Lisna Sari","doi":"10.31253/algor.v4i1.1850","DOIUrl":"https://doi.org/10.31253/algor.v4i1.1850","url":null,"abstract":"Sistem pemerintahan dan pelayanan publik yang bersih, transparan, merupakan tantangan yang harus dijawab oleh lembaga pemerintahan dalam menjalankan fungsinya. Dengan semangat itulah Kabupaten Tanggamus akan membangun infarstruktur jaringan online sampai ke tingkat desa. Dengan sarana infrastruktur yang telah tersedia dan permasalahan administrasi dan potensi desa yang perlu mendapatkan perhatian serius, mendorong penulis untuk memamfaatkan infrastruktur yang ada dengan mengisi konten / membangun aplikasi yang bersifat e-Government. Seringnya permintaan data tentang perangkat desa dan potensi desa oleh para pimpinan instansi pemerintahan yang lebih tinggi, yang dilakukan secara manual tidak menutup kemungkinan data-data yang disampaikan kurang akurat ataupun kurang cepat, lagipula adanya potensi-potensi desa yang belum optimal serta terjadinya perubahan data-data di desa perlu mendapatkan perhatian yang serius semua pihak. Penulis melakukan penelitian dengan membangun aplikasi yang bertema “Analisa Perancangan Sistem Informasi Perkembangan Desa Sridadi Kecamatan Wonosobo di Pemerintah Kabupaten Tanggamus”. Pengembangan sistem dilakukan berdasarkan pendekatan metode System Development Life Cycle (SDLC) yang meliputi tahapan-tahapan perencanaan, analisis, desain, dan implementasi sistem. Metode pengumpulan data dilakukan dengan cara observasi,wawancara dan studi Pustaka, Sistem informasi yang akan penulis bangun berbasis web dengan bahasa pemprograman PHP, aplikasi dan database terpusat di server dan dapat diakses langsung dari desa.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"158 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80135944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implementasi Speech Recognition untuk Asisten Virtual dengan Python","authors":"Y. Setyawan, Yo Ceng Giap","doi":"10.31253/algor.v4i1.1545","DOIUrl":"https://doi.org/10.31253/algor.v4i1.1545","url":null,"abstract":"Cara berkomunikasi yang paling umum digunakan oleh manusia adalah suara atau ucapan. Banyak eksperimen yang dilakukan di aspek pemrosesan suara untuk menciptakan model mekanis yang mensimulasikan bagaimana cara manusia berkomunikasi secara verbal. Teknologi pengenalan suara bertujuan untuk mengembangkan sistem dan teknik tentang bagaimana mengenalkan perintah berbentuk suara agar dapat dimengerti oleh mesin, sehingga mesin mampu menjalankan perintah yang diberikan. Penelitian ini menggunakan teknologi pengenalan suara untuk diimplemetasikan ke aplikasi asisten virtual pribadi berbasiskan desktop dengan tujuan membantu menyederhanakan tugas sehari-hari melalui komputer. Hasil penelitian ini menghasilkan sebuah aplikasi pengenalan suara (speech recognition) untuk menjalankan tugas umum tertentu di desktop dan menyalakan perangkat elektronik. Dari pengujian yang sudah dilakukan, aplikasi dapat mengenali perintah suara untuk menjalankan perintah yang diberikan dan dapat menyalakan ataupun mematikan perangkat listrik seperti yang diharapkan.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"59 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81923896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"APLIKASI KLASIFIKASI KEPRIBADIAN MANUSIA MENGGUNAKAN ALGORITMA TREE DECISION (C4.5) BERBASIS WEB","authors":"Kent Christopher, Desiyanna Lasut, L. Kusuma","doi":"10.31253/algor.v4i1.1744","DOIUrl":"https://doi.org/10.31253/algor.v4i1.1744","url":null,"abstract":"Dalam kehidupan sehari hari setiap manusia memiliki sifat dan kepribadian yang unik dan berbeda setiap orangnya. Daripada itu, sangatlah penting untuk mengetahui kepribadian kita sejak usia dini. Kebutuhan akan layanan informasi sangat tinggi dan memprediksi karakter manusia dapat dilakukan secara manual, namun aplikasi yang menggunakan metode data mining dapat menyederhanakan proses prediksi karakter manusia, sehingga tidak memerlukan waktu pemrosesan terlalu lama. Saat ini masih banyak orang yang tidak mengetahui apa kepribadian mereka, Pembuatan aplikasi ini dimaksud untuk memudahkah orang dalam menemukan kepribadian dalam diri sehingga bisa mengetahui apa potensi , kelebihan dan kekurangan yang di miliki. Algoritma C4.5 memiliki model prediktif dengan akurasi dan memiliki kemampuan untuk pengambilan keputusan yang rumit diubah jadi lebih mudah, sehingga pemilihan keputusan akan lebih tepat, Sehingga algoritma C4.5 dapat mengklasifikasikan kepribadian yang di miliki oleh orang orang. Tujuan dari aplikasi ini adalah Membantu seseorang dalam mengetahui jenis kepribadian yang di miliki.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73912289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rancang Bangun Sistem Keamanan Door Lock Menggunakan E-Ktp Berbasis Arduino Wemos Esp8266","authors":"DICKA RIFQI AZZIZI, Rino","doi":"10.31253/algor.v4i1.1742","DOIUrl":"https://doi.org/10.31253/algor.v4i1.1742","url":null,"abstract":"Tujuan dari penelitian ini adalah untuk membangun sebuah pintu pengaman yang menggunakan sistem E-KTP sebagai ID card dan juga sebagai pengganti kunci pintu manual atau tradisional, dan Arduino sebagai pengontrol rangkaian. Menggunakan kunci tradisional membuat mereka lebih rentan terhadap pencurian. Oleh karena itu, peneliti menggunakan E-KTP sebagai kunci elektronik yang lebih efektif untuk pengguna. Saat E-KTP menggantikan kunci tradisional, membuka pintu menjadi lebih mudah. Kunci elektronik menggantikan kunci pintu manual dengan kunci elektronik. Kunci pintu pintar dapat dioperasikan dengan keypad, sidik jari, dan juga dapat menggunakan perintah dengan sensor suara, remote control, dan bahkan IoT. prototipe dibuat menggunakan metode waterfall. Metode langkah demi langkah ini bekerja sebagai berikut: Mengumpulkan serangkaian proses yang dapat dieksekusi satu demi satu. Dari pengumpulan data, desain prototipe, pembuatan prototipe, pengujian prototipe, pengujian prototipe hingga penyelesaian. Dari hasil penelitian dan pembahasan dapat disimpulkan bahwa E-KTP kunci pintu dapat dibangun dan dikendalikan menggunakan","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"2009 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82586588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}