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Penerapan Data Mining Untuk Merekomendasikan Seri Produk NAS Kepada Calon Konsumen Toko Storage Menggunakan Algoritma Multinomial Naïve Bayes 数据挖掘应用商店推荐消费者对未来的NAS产品系列存储使用‘Multinomial¯有一个贝叶斯算法
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-09-15 DOI: 10.31253/algor.v4i1.1498
Fernando Verdy Sunata, S. Hariyanto, Dicky Surya Dwi Putra, Hartana Wijaya
{"title":"Penerapan Data Mining Untuk Merekomendasikan Seri Produk NAS Kepada Calon Konsumen Toko Storage Menggunakan Algoritma Multinomial Naïve Bayes","authors":"Fernando Verdy Sunata, S. Hariyanto, Dicky Surya Dwi Putra, Hartana Wijaya","doi":"10.31253/algor.v4i1.1498","DOIUrl":"https://doi.org/10.31253/algor.v4i1.1498","url":null,"abstract":"Toko Storage merupakan nama dagang yang digunakan oleh PT. Distributor Trimitra Indonesia untuk menjual berbagai macam produk NAS (Network Attached Storage). Banyaknya produk NAS yang dijual dengan harga dan spesifikasi yang berbeda-beda, terkadang membuat bingung bahkan membuat calon konsumen kesulitan dalam memilih produk NAS yang tepat. Sehingga tidak jarang dari mereka yang bertanya mengenai rekomendasi NAS kepada admin toko. Proses pemberian rekomendasi dilakukan melalui sesi tanya jawab terkait dengan kebutuhan NAS. Proses pemberian rekomendasi terkadang memakan waktu yang lama karena harus menunggu jawaban dari calon konsumen. Karena itu, dilakukan penelitian yang bertujuan untuk merancang sebuah sistem yang mampu memberikan rekomendasi seri produk NAS kepada calon konsumen dengan menerapkan metode data mining dan algoritma multinomial naïve bayes (MNB). Hasil dari penerapan metode dan algoritma yang digunakan terbukti berhasil diimplementasikan pada data yang digunakan, hal ini dibuktikan dari hasil pengujian dan evaluasi yang dilakukan menggunakan bantuan aplikasi Weka yang menghasilkan nilai akurasi sebesar 95,5556%. Hasil akhir dari penelitian ini berupa rancangan sistem rekomendasi seri produk NAS berbasis web yang dapat digunakan oleh pengguna untuk mendapatkan rekomendasi seri produk NAS secara cepat dan tepat, hanya dengan memasukan kriteria NAS yang dicari.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"147 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77642366","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}
引用次数: 0
On the clique number of noisy random geometric graphs 噪声随机几何图的团数
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-08-22 DOI: 10.1002/rsa.21134
Matthew Kahle, Minghao Tian, Yusu Wang
{"title":"On the clique number of noisy random geometric graphs","authors":"Matthew Kahle, Minghao Tian, Yusu Wang","doi":"10.1002/rsa.21134","DOIUrl":"https://doi.org/10.1002/rsa.21134","url":null,"abstract":"Let Gn$$ {G}_n $$ be a random geometric graph, and then for q,p∈[0,1)$$ q,pin left[0,1right) $$ we construct a (q,p)$$ left(q,pright) $$ ‐perturbed noisy random geometric graph Gnq,p$$ {G}_n^{q,p} $$ where each existing edge in Gn$$ {G}_n $$ is removed with probability q$$ q $$ , while and each non‐existent edge in Gn$$ {G}_n $$ is inserted with probability p$$ p $$ . We give asymptotically tight bounds on the clique number ωGnq,p$$ omega left({G}_n^{q,p}right) $$ for several regimes of parameter.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"61 1 1","pages":"242 - 279"},"PeriodicalIF":1.0,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90136056","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}
引用次数: 3
The number of bounded‐degree spanning trees 有界度生成树的数目
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-07-29 DOI: 10.1002/rsa.21118
R. Yuster
{"title":"The number of bounded‐degree spanning trees","authors":"R. Yuster","doi":"10.1002/rsa.21118","DOIUrl":"https://doi.org/10.1002/rsa.21118","url":null,"abstract":"For a graph G$$ G $$ , let ck(G)$$ {c}_k(G) $$ be the number of spanning trees of G$$ G $$ with maximum degree at most k$$ k $$ . For k≥3$$ kge 3 $$ , it is proved that every connected n$$ n $$ ‐vertex r$$ r $$ ‐regular graph G$$ G $$ with r≥nk+1$$ rge frac{n}{k+1} $$ satisfies ck(G)1/n≥(1−on(1))r·zk,$$ {c}_k{(G)}^{1/n}ge left(1-{o}_n(1)right)rcdotp {z}_k, $$where zk>0$$ {z}_k>0 $$ approaches 1 extremely fast (e.g., z10=0.999971$$ {z}_{10}=0.999971 $$ ). The minimum degree requirement is essentially tight as for every k≥2$$ kge 2 $$ there are connected n$$ n $$ ‐vertex r$$ r $$ ‐regular graphs G$$ G $$ with r=⌊n/(k+1)⌋−2$$ r=leftlfloor n/left(k+1right)rightrfloor -2 $$ for which ck(G)=0$$ {c}_k(G)=0 $$ . Regularity may be relaxed, replacing r$$ r $$ with the geometric mean of the degree sequence and replacing zk$$ {z}_k $$ with zk∗>0$$ {z}_k^{ast }>0 $$ that also approaches 1, as long as the maximum degree is at most n(1−(3+ok(1))lnk/k)$$ nleft(1-left(3+{o}_k(1)right)sqrt{ln k/k}right) $$ . The same holds with no restriction on the maximum degree as long as the minimum degree is at least nk(1+ok(1))$$ frac{n}{k}left(1+{o}_k(1)right) $$ .","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"45 1","pages":"737 - 757"},"PeriodicalIF":1.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83945251","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}
引用次数: 0
Heilbronn triangle‐type problems in the unit square [0,1]2 单位平方中的Heilbronn三角形型问题[0,1
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-07-25 DOI: 10.1002/rsa.21109
F. Benevides, C. Hoppen, H. Lefmann, Knut Odermann
{"title":"Heilbronn triangle‐type problems in the unit square [0,1]2","authors":"F. Benevides, C. Hoppen, H. Lefmann, Knut Odermann","doi":"10.1002/rsa.21109","DOIUrl":"https://doi.org/10.1002/rsa.21109","url":null,"abstract":"The Heilbronn triangle problem is a classical geometrical problem that asks for a placement of n$$ n $$ points in the unit square [0,1]2$$ {left[0,1right]}^2 $$ that maximizes the smallest area of a triangle formed by three of those points. This problem has natural generalizations. For an integer k≥3$$ kge 3 $$ and a set 𝒫 of n$$ n $$ points in [0,1]2$$ {left[0,1right]}^2 $$ , let Ak(𝒫) be the minimum area of the convex hull of k$$ k $$ points in 𝒫 . Here, instead of considering the supremum of Ak(𝒫) over all such choices of 𝒫 , we consider its average value, Δ˜k(n)$$ {tilde{Delta}}_k(n) $$ , when the n$$ n $$ points in 𝒫 are chosen independently and uniformly at random in [0,1]2$$ {left[0,1right]}^2 $$ . We prove that Δ˜k(n)=Θn−kk−2$$ {tilde{Delta}}_k(n)=Theta left({n}^{frac{-k}{k-2}}right) $$ , for every fixed k≥3$$ kge 3 $$ .","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"37 1","pages":"585 - 599"},"PeriodicalIF":1.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79762642","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}
引用次数: 0
Voter models on subcritical scale‐free random graphs 亚临界无标度随机图上的选民模型
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-07-23 DOI: 10.1002/rsa.21107
J. Fernley, Marcel Ortgiese
{"title":"Voter models on subcritical scale‐free random graphs","authors":"J. Fernley, Marcel Ortgiese","doi":"10.1002/rsa.21107","DOIUrl":"https://doi.org/10.1002/rsa.21107","url":null,"abstract":"The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyze the time to consensus for the voter model when the underlying graph is a subcritical scale‐free random graph. Moreover, we generalize the model to include a “temperature” parameter controlling how the graph influences the speed of opinion change. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Finally, we also consider a discursive voter model, where voters discuss their opinions with their neighbors. Our proofs rely on the well‐known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"18 1","pages":"376 - 429"},"PeriodicalIF":1.0,"publicationDate":"2022-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85329357","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}
引用次数: 2
Expansion of random 0/1 polytopes 随机0/1多面体的展开
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-07-08 DOI: 10.1002/rsa.21184
Brett Leroux, Luis Rademacher
{"title":"Expansion of random 0/1 polytopes","authors":"Brett Leroux, Luis Rademacher","doi":"10.1002/rsa.21184","DOIUrl":"https://doi.org/10.1002/rsa.21184","url":null,"abstract":"A conjecture of Milena Mihail and Umesh Vazirani (Proc. 24th Annu. ACM Symp. Theory Comput., ACM, Victoria, BC, 1992, pp. 26–38.) states that the edge expansion of the graph of every polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a polytope in is greater than one over some polynomial function of . This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of a random polytope in is at least with high probability.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"51 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90923425","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}
引用次数: 1
Cycle lengths in randomly perturbed graphs 随机摄动图中的周期长度
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-06-24 DOI: 10.1002/rsa.21170
Elad Aigner-Horev, Dan Hefetz, M. Krivelevich
{"title":"Cycle lengths in randomly perturbed graphs","authors":"Elad Aigner-Horev, Dan Hefetz, M. Krivelevich","doi":"10.1002/rsa.21170","DOIUrl":"https://doi.org/10.1002/rsa.21170","url":null,"abstract":"Let G$$ G $$ be an n$$ n $$ ‐vertex graph, where δ(G)≥δn$$ delta (G)ge delta n $$ for some δ:=δ(n)$$ delta := delta (n) $$ . A result of Bohman, Frieze and Martin from 2003 asserts that if α(G)=Oδ2n$$ alpha (G)=Oleft({delta}^2nright) $$ , then perturbing G$$ G $$ via the addition of ωlog(1/δ)δ3$$ omega left(frac{log left(1/delta right)}{delta^3}right) $$ random edges, a.a.s. yields a Hamiltonian graph. We prove several improvements and extensions of the aforementioned result. In particular, keeping the bound on α(G)$$ alpha (G) $$ as above and allowing for δ=Ω(n−1/3)$$ delta =Omega left({n}^{-1/3}right) $$ , we determine the correct order of magnitude of the number of random edges whose addition to G$$ G $$ a.a.s. yields a pancyclic graph. Moreover, we prove similar results for sparser graphs, and assuming the correctness of Chvátal's toughness conjecture, we handle graphs having larger independent sets. Finally, under milder conditions, we determine the correct order of magnitude of the number of random edges whose addition to G$$ G $$ a.a.s. yields a graph containing an almost spanning cycle.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"62 1","pages":"867 - 884"},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74130827","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}
引用次数: 4
A fourth‐moment phenomenon for asymptotic normality of monochromatic subgraphs 单色子图渐近正态性的一个四矩现象
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-05-09 DOI: 10.1002/rsa.21166
Sayan Das, Z. Himwich, Nitya Mani
{"title":"A fourth‐moment phenomenon for asymptotic normality of monochromatic subgraphs","authors":"Sayan Das, Z. Himwich, Nitya Mani","doi":"10.1002/rsa.21166","DOIUrl":"https://doi.org/10.1002/rsa.21166","url":null,"abstract":"Given a graph sequence {Gn}n≥1$$ {left{{G}_nright}}_{nge 1} $$ and a simple connected subgraph H$$ H $$ , we denote by T(H,Gn)$$ Tleft(H,{G}_nright) $$ the number of monochromatic copies of H$$ H $$ in a uniformly random vertex coloring of Gn$$ {G}_n $$ with c≥2$$ cge 2 $$ colors. We prove a central limit theorem for T(H,Gn)$$ Tleft(H,{G}_nright) $$ (we denote the appropriately centered and rescaled statistic as Z(H,Gn)$$ Zleft(H,{G}_nright) $$ ) with explicit error rates. The error rates arise from graph counts of collections formed by joining copies of H$$ H $$ which we call good joins. Good joins are closely related to the fourth moment of Z(H,Gn)$$ Zleft(H,{G}_nright) $$ , which allows us to show a fourth moment phenomenon for the central limit theorem. For c≥30$$ cge 30 $$ , we show that Z(H,Gn)$$ Zleft(H,{G}_nright) $$ converges in distribution to 𝒩(0,1) whenever its fourth moment converges to 3. We show the convergence of the fourth moment is necessary to obtain a normal limit when c≥2$$ cge 2 $$ .","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"80 1","pages":"968 - 996"},"PeriodicalIF":1.0,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91143161","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}
引用次数: 0
Independence number of hypergraphs under degree conditions 度条件下超图的独立数
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-05-05 DOI: 10.1002/rsa.21151
V. Rödl, M. Sales, Yi Zhao
{"title":"Independence number of hypergraphs under degree conditions","authors":"V. Rödl, M. Sales, Yi Zhao","doi":"10.1002/rsa.21151","DOIUrl":"https://doi.org/10.1002/rsa.21151","url":null,"abstract":"A well‐known result of Ajtai Komlós, Pintz, Spencer, and Szemerédi (J. Combin. Theory Ser. A 32 (1982), 321–335) states that every k$$ k $$ ‐graph H$$ H $$ on n$$ n $$ vertices, with girth at least five, and average degree tk−1$$ {t}^{k-1} $$ contains an independent set of size cn(logt)1/(k−1)/t$$ cn{left(log tright)}^{1/left(k-1right)}/t $$ for some c>0$$ c>0 $$ . In this paper we show that an independent set of the same size can be found under weaker conditions allowing certain cycles of length 2, 3, and 4. Our work is motivated by a problem of Lo and Zhao, who asked for k≥4$$ kge 4 $$ , how large of an independent set a k$$ k $$ ‐graph H$$ H $$ on n$$ n $$ vertices necessarily has when its maximum (k−2)$$ left(k-2right) $$ ‐degree Δk−2(H)≤dn$$ {Delta}_{k-2}(H)le dn $$ . (The corresponding problem with respect to (k−1)$$ left(k-1right) $$ ‐degrees was solved by Kostochka, Mubayi, and Verstraëte (Random Struct. & Algorithms 44 (2014), 224–239).) In this paper we show that every k$$ k $$ ‐graph H$$ H $$ on n$$ n $$ vertices with Δk−2(H)≤dn$$ {Delta}_{k-2}(H)le dn $$ contains an independent set of size cndloglognd1/(k−1)$$ c{left(frac{n}{d}mathrm{loglog}frac{n}{d}right)}^{1/left(k-1right)} $$ , and under additional conditions, an independent set of size cndlognd1/(k−1)$$ c{left(frac{n}{d}log frac{n}{d}right)}^{1/left(k-1right)} $$ . The former assertion gives a new upper bound for the (k−2)$$ left(k-2right) $$ ‐degree Turán density of complete k$$ k $$ ‐graphs.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"6 1","pages":"821 - 863"},"PeriodicalIF":1.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83050585","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}
引用次数: 0
Limit theorems for patterns in ranked tree‐child networks 秩树子网络中模式的极限定理
IF 1 3区 数学
Random Structures & Algorithms Pub Date : 2022-04-15 DOI: 10.1002/rsa.21177
Michael Fuchs, Hexuan Liu, Tsan-Cheng Yu
{"title":"Limit theorems for patterns in ranked tree‐child networks","authors":"Michael Fuchs, Hexuan Liu, Tsan-Cheng Yu","doi":"10.1002/rsa.21177","DOIUrl":"https://doi.org/10.1002/rsa.21177","url":null,"abstract":"We prove limit laws for the number of occurrences of a pattern on the fringe of a ranked tree-child network which is picked uniformly at random. Our results extend the limit law for cherries proved by Bienvenu et al. (2022). For patterns of height $1$ and $2$, we show that they either occur frequently (mean is asymptotically linear and limit law is normal) or sporadically (mean is asymptotically constant and limit law is Poisson) or not all (mean tends to $0$ and limit law is degenerate). We expect that these are the only possible limit laws for any fringe pattern.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83529908","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}
引用次数: 1
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