Pub Date : 2012-11-18DOI: 10.1080/15427951.2013.814092
D. Gleich, Ryan A. Rossi
Abstract We propose a dynamical system that captures changes to the network centrality of nodes as external interest in those nodes varies. We derive this system by adding time-dependent teleportation to the PageRank score. The result is not a single set of importance scores, but rather a time-dependent set. These can be converted into ranked lists in a variety of ways, for instance, by taking the largest change in the importance score. For an interesting class of dynamic teleportation functions, we derive closed-form solutions for the dynamic PageRank vector. The magnitude of the deviation from a static PageRank vector is given by a PageRank problem with complex-valued teleportation parameters. Moreover, these dynamical systems are easy to evaluate. We demonstrate the utility of dynamic teleportation on both the article graph of Wikipedia, where the external interest information is given by the number of hourly visitors to each page, and the Twitter social network, where external interest is the number of tweets per month. For these problems, we show that using information from the dynamical system helps improve a prediction task and identify trends in the data.
摘要:我们提出了一个动态系统，它可以捕捉到节点的网络中心性随着外部兴趣的变化而变化。我们通过在PageRank分数中添加时间相关的传送来推导这个系统。结果不是一个单一的重要性分数集合，而是一个与时间相关的集合。这些可以通过各种方式转换成排名列表，例如，通过在重要性得分中取最大的变化。对于一类有趣的动态传送函数，我们导出了动态PageRank向量的封闭解。通过一个具有复值隐形传态参数的PageRank问题，给出了与静态PageRank向量偏差的大小。此外，这些动力系统易于评估。我们在维基百科(Wikipedia)的文章图和Twitter社交网络(Twitter social network)上展示了动态传送的效用，前者的外部兴趣信息由每小时访问每个页面的人数给出，后者的外部兴趣是每月的推文数量。对于这些问题，我们表明使用来自动态系统的信息有助于改进预测任务并识别数据中的趋势。
{"title":"A Dynamical System for PageRank with Time-Dependent Teleportation","authors":"D. Gleich, Ryan A. Rossi","doi":"10.1080/15427951.2013.814092","DOIUrl":"https://doi.org/10.1080/15427951.2013.814092","url":null,"abstract":"Abstract We propose a dynamical system that captures changes to the network centrality of nodes as external interest in those nodes varies. We derive this system by adding time-dependent teleportation to the PageRank score. The result is not a single set of importance scores, but rather a time-dependent set. These can be converted into ranked lists in a variety of ways, for instance, by taking the largest change in the importance score. For an interesting class of dynamic teleportation functions, we derive closed-form solutions for the dynamic PageRank vector. The magnitude of the deviation from a static PageRank vector is given by a PageRank problem with complex-valued teleportation parameters. Moreover, these dynamical systems are easy to evaluate. We demonstrate the utility of dynamic teleportation on both the article graph of Wikipedia, where the external interest information is given by the number of hourly visitors to each page, and the Twitter social network, where external interest is the number of tweets per month. For these problems, we show that using information from the dynamical system helps improve a prediction task and identify trends in the data.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"10 1","pages":"188 - 217"},"PeriodicalIF":0.0,"publicationDate":"2012-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2013.814092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-26DOI: 10.1080/15427951.2012.728100
H. Boche, Brendan Farrell
High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and out-of-band radiation. However, reducing peak values generally comes at the cost of some other resource. We provide a theoretical contribution toward understanding the relationship between peak value reduction and the resulting cost in information rates. In particular, we address the relationship between peak values and the proportion of transmission signals allocated for information transmission when one is using a strategy known as tone reservation. We show that when tone reservation is used in both OFDM and DS-CDMA systems, if a peak-to-average power ratio criterion is always satisfied, then the proportion of transmission signals that may be allocated for information transmission must tend to zero. We investigate properties of these two systems for sets of both finite and infinite cardinalities. We present properties that OFDM and DS-CDMA share in common as well as ways in which they fundamentally differ.
{"title":"On the Peak-to-Average Power Ratio Reduction Problem for Orthogonal Transmission Schemes","authors":"H. Boche, Brendan Farrell","doi":"10.1080/15427951.2012.728100","DOIUrl":"https://doi.org/10.1080/15427951.2012.728100","url":null,"abstract":"High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and out-of-band radiation. However, reducing peak values generally comes at the cost of some other resource. We provide a theoretical contribution toward understanding the relationship between peak value reduction and the resulting cost in information rates. In particular, we address the relationship between peak values and the proportion of transmission signals allocated for information transmission when one is using a strategy known as tone reservation. We show that when tone reservation is used in both OFDM and DS-CDMA systems, if a peak-to-average power ratio criterion is always satisfied, then the proportion of transmission signals that may be allocated for information transmission must tend to zero. We investigate properties of these two systems for sets of both finite and infinite cardinalities. We present properties that OFDM and DS-CDMA share in common as well as ways in which they fundamentally differ.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"9 1","pages":"265 - 296"},"PeriodicalIF":0.0,"publicationDate":"2012-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.728100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-01DOI: 10.1080/15427951.2012.654480
Maochao Xu, Shouhuai Xu
Abstract Quantitative security analysis of networked computer systems has been an open problem in computer security for decades. Recently, a promising approach was proposed in [Li et al. 11], which, however, made some strong assumptions including the exponential distribution of, and the independence among, the relevant random variables. In this paper, we substantially weaken these assumptions while offering, in addition to the same types of analytical results as in [Li et al. 11], methods for obtaining the desired security quantities in practice. Moreover, we investigate the problem from a higher-level abstraction, which also leads to both analytical results and practical methods for obtaining the desired security quantities. These should represent a significant step toward ultimately solving the problem of quantitative security analysis of networked computer systems.
网络计算机系统的定量安全分析一直是计算机安全领域的一个开放性问题。最近，[Li et al. 11]提出了一种很有前途的方法，然而，该方法做出了一些强有力的假设，包括相关随机变量的指数分布和相互之间的独立性。在本文中，我们大大削弱了这些假设，同时除了提供与[Li et al. 11]中相同类型的分析结果外，还提供了在实践中获得所需安全量的方法。此外，我们从一个更高层次的抽象来研究这个问题，这也导致了获得期望安全量的分析结果和实用方法。这些应该是朝着最终解决联网计算机系统的定量安全分析问题迈出的重要一步。
{"title":"An Extended Stochastic Model for Quantitative Security Analysis of Networked Systems","authors":"Maochao Xu, Shouhuai Xu","doi":"10.1080/15427951.2012.654480","DOIUrl":"https://doi.org/10.1080/15427951.2012.654480","url":null,"abstract":"Abstract Quantitative security analysis of networked computer systems has been an open problem in computer security for decades. Recently, a promising approach was proposed in [Li et al. 11], which, however, made some strong assumptions including the exponential distribution of, and the independence among, the relevant random variables. In this paper, we substantially weaken these assumptions while offering, in addition to the same types of analytical results as in [Li et al. 11], methods for obtaining the desired security quantities in practice. Moreover, we investigate the problem from a higher-level abstraction, which also leads to both analytical results and practical methods for obtaining the desired security quantities. These should represent a significant step toward ultimately solving the problem of quantitative security analysis of networked computer systems.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"8 1","pages":"288 - 320"},"PeriodicalIF":0.0,"publicationDate":"2012-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.654480","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-06-22DOI: 10.1080/15427951.2013.819210
C. Cooper, T. Radzik, Yiannis Siantos
Abstract We develop a fast method for finding all high-degree vertices of a connected graph with a power-law degree sequence. The method uses a biased random walk, where the bias is a function of the power law c of the degree sequence. Let G(t) be a t-vertex graph, with degree sequence power law c ≥ 3 generated by a generalized preferential attachment process that adds m edges at each step. Let Sa be the set of all vertices of degree at least ta in G(t). We analyze a biased random walk that makes transitions along undirected edges {x, y} with probabilities proportional to (d(x)d(y))b, where d(x) is the degree of vertex x and b > 0 is a constant parameter. With parameter b = (c − 1)(c − 2)/(2c − 3), the random walk discovers the set Sa completely in steps with high probability. The error parameter ε depends on c, a, and m. The cover time of the entire graph G(t) by the biased walk is . Thus the expected time to discover all vertices by the biased walk is not much higher than the Θ(tlog t) cover time of a simple random walk. The standard preferential attachment process generates graphs with power law c = 3. The search parameter b = 2/3 is appropriate for such graphs. We conduct experimental tests on a preferential attachment graph and on a sample of the underlying graph of the World Wide Web with power law c ≈ 3 that support the claimed property.
{"title":"A Fast Algorithm to Find All High-Degree Vertices in Graphs with a Power-Law Degree Sequence","authors":"C. Cooper, T. Radzik, Yiannis Siantos","doi":"10.1080/15427951.2013.819210","DOIUrl":"https://doi.org/10.1080/15427951.2013.819210","url":null,"abstract":"Abstract We develop a fast method for finding all high-degree vertices of a connected graph with a power-law degree sequence. The method uses a biased random walk, where the bias is a function of the power law c of the degree sequence. Let G(t) be a t-vertex graph, with degree sequence power law c ≥ 3 generated by a generalized preferential attachment process that adds m edges at each step. Let Sa be the set of all vertices of degree at least ta in G(t). We analyze a biased random walk that makes transitions along undirected edges {x, y} with probabilities proportional to (d(x)d(y))b, where d(x) is the degree of vertex x and b > 0 is a constant parameter. With parameter b = (c − 1)(c − 2)/(2c − 3), the random walk discovers the set Sa completely in steps with high probability. The error parameter ε depends on c, a, and m. The cover time of the entire graph G(t) by the biased walk is . Thus the expected time to discover all vertices by the biased walk is not much higher than the Θ(tlog t) cover time of a simple random walk. The standard preferential attachment process generates graphs with power law c = 3. The search parameter b = 2/3 is appropriate for such graphs. We conduct experimental tests on a preferential attachment graph and on a sample of the underlying graph of the World Wide Web with power law c ≈ 3 that support the claimed property.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"62 1","pages":"137 - 161"},"PeriodicalIF":0.0,"publicationDate":"2012-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2013.819210","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-06-22DOI: 10.1080/15427951.2013.800005
F. Graham, Wenbo Zhao, Mark Kempton
Abstract Many problems arising in dealing with high-dimensional data sets involve connection graphs in which each edge is associated with both an edge weight and a d-dimensional linear transformation. We consider vectorized versions of PageRank and effective resistance that can be used as basic tools for organizing and analyzing complex data sets. For example, generalized PageRank and effective resistance can be utilized to derive and modify diffusion distances for vector diffusion maps in data and image processing. Furthermore, the edge-ranking of the connection graphs determined by vectorized PageRank and effective resistance are an essential part of sparsification algorithms that simplify and preserve the global structure of connection graphs. In addition, we examine consistencies in a connection graph, particularly in the applications of recovering low-dimensional data sets and the reduction of noise. In these applications, we analyze the effect of deleting edges with high edge rank.
{"title":"Ranking and Sparsifying a Connection Graph","authors":"F. Graham, Wenbo Zhao, Mark Kempton","doi":"10.1080/15427951.2013.800005","DOIUrl":"https://doi.org/10.1080/15427951.2013.800005","url":null,"abstract":"Abstract Many problems arising in dealing with high-dimensional data sets involve connection graphs in which each edge is associated with both an edge weight and a d-dimensional linear transformation. We consider vectorized versions of PageRank and effective resistance that can be used as basic tools for organizing and analyzing complex data sets. For example, generalized PageRank and effective resistance can be utilized to derive and modify diffusion distances for vector diffusion maps in data and image processing. Furthermore, the edge-ranking of the connection graphs determined by vectorized PageRank and effective resistance are an essential part of sparsification algorithms that simplify and preserve the global structure of connection graphs. In addition, we examine consistencies in a connection graph, particularly in the applications of recovering low-dimensional data sets and the reduction of noise. In these applications, we analyze the effect of deleting edges with high edge rank.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"10 1","pages":"115 - 87"},"PeriodicalIF":0.0,"publicationDate":"2012-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2013.800005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-06-22DOI: 10.1080/15427951.2013.833676
F. Graham, Alexander Tsiatas
Abstract We analyze a network coloring game on hypergraphs that can also describe a voter model. Each node represents a voter and is colored according to its preferred candidate (or undecided). Each hyperedge is a subset of voters that can interact and influence one another. In each round of the game, one hyperedge is chosen randomly, and the voters in the hyperedge can change their colors according to some prescribed probability distribution. We analyze this interaction model based on random walks on the associated weighted directed state graph. Under certain “memoryless” restrictions, we can use semigroup spectral methods to explicitly determine the spectrum of the state graph, and the random walk on the state graph converges to its stationary distribution in O(mlog n) steps, where n is the number of voters and m the number of hyperedges. We can then estimate probabilities that events occur within an error bound of ε by simulating the voting game for O(log (1/ε)mlog n) rounds. We also consider a partially memoryless game using the memoryless game for comparison and analysis, which serves as an approximation of the actual interaction dynamics.
{"title":"Hypergraph Coloring Games and Voter Models","authors":"F. Graham, Alexander Tsiatas","doi":"10.1080/15427951.2013.833676","DOIUrl":"https://doi.org/10.1080/15427951.2013.833676","url":null,"abstract":"Abstract We analyze a network coloring game on hypergraphs that can also describe a voter model. Each node represents a voter and is colored according to its preferred candidate (or undecided). Each hyperedge is a subset of voters that can interact and influence one another. In each round of the game, one hyperedge is chosen randomly, and the voters in the hyperedge can change their colors according to some prescribed probability distribution. We analyze this interaction model based on random walks on the associated weighted directed state graph. Under certain “memoryless” restrictions, we can use semigroup spectral methods to explicitly determine the spectrum of the state graph, and the random walk on the state graph converges to its stationary distribution in O(mlog n) steps, where n is the number of voters and m the number of hyperedges. We can then estimate probabilities that events occur within an error bound of ε by simulating the voting game for O(log (1/ε)mlog n) rounds. We also consider a partially memoryless game using the memoryless game for comparison and analysis, which serves as an approximation of the actual interaction dynamics.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"10 1","pages":"66 - 86"},"PeriodicalIF":0.0,"publicationDate":"2012-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2013.833676","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-06-22DOI: 10.1080/15427951.2013.796301
C. Cooper, A. Frieze, P. Prałat
Abstract We investigate a stochastic model for complex networks, based on a spatial embedding of the nodes, called the spatial preferred attachment (SPA) model. In the SPA model, nodes have spheres of influence of varying sizes, and a new node may link to a node only if it falls within its region of influence. The spatial embedding of the nodes models the background knowledge or identity of the node, which influences its link environment. In this paper, we focus on the (directed) diameter, small separators, and the (weak) giant component of the model.
{"title":"Some Typical Properties of the Spatial Preferred Attachment Model","authors":"C. Cooper, A. Frieze, P. Prałat","doi":"10.1080/15427951.2013.796301","DOIUrl":"https://doi.org/10.1080/15427951.2013.796301","url":null,"abstract":"Abstract We investigate a stochastic model for complex networks, based on a spatial embedding of the nodes, called the spatial preferred attachment (SPA) model. In the SPA model, nodes have spheres of influence of varying sizes, and a new node may link to a node only if it falls within its region of influence. The spatial embedding of the nodes models the background knowledge or identity of the node, which influences its link environment. In this paper, we focus on the (directed) diameter, small separators, and the (weak) giant component of the model.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"43 1","pages":"116 - 136"},"PeriodicalIF":0.0,"publicationDate":"2012-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2013.796301","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59946967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-03-27DOI: 10.1080/15427951.2012.749437
Weituo Zhang, C. Lim
We propose a general form of community-detecting functions for finding communities—an optimal partition of a random network—and examine the concentration and stability of the function values using the bounded difference martingale method. We derive LDP inequalities for both the general case and several specific community-detecting functions: modularity, graph bipartitioning, and q-Potts community structure. We also discuss the concentration and stability of community-detecting functions on different types of random networks: sparse and nonsparse networks and some examples such as ER and CL networks.
{"title":"Concentration and Stability of Community-Detecting Functions on Random Networks","authors":"Weituo Zhang, C. Lim","doi":"10.1080/15427951.2012.749437","DOIUrl":"https://doi.org/10.1080/15427951.2012.749437","url":null,"abstract":"We propose a general form of community-detecting functions for finding communities—an optimal partition of a random network—and examine the concentration and stability of the function values using the bounded difference martingale method. We derive LDP inequalities for both the general case and several specific community-detecting functions: modularity, graph bipartitioning, and q-Potts community structure. We also discuss the concentration and stability of community-detecting functions on different types of random networks: sparse and nonsparse networks and some examples such as ER and CL networks.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"9 1","pages":"360 - 383"},"PeriodicalIF":0.0,"publicationDate":"2012-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.749437","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-03-01DOI: 10.1080/15427951.2012.635562
A. Bonato, Ravi Kumar, D. Sivakumar
This issue of Internet Mathematics includes a selection of papers that were presented at the Seventh Workshop on Algorithms and Models for the Web-Graph, WAW 2010, held at Stanford University in December 2010. The papers in this issue, unlike the conference proceedings of the workshop, do not have page limits and contain full versions of proofs and algorithms. All the articles have been thoroughly reviewed in accordance with the usual high standards of Internet Mathematics. The papers address a number of topics related to complex networks such as network-creation games, applications of PageRank, efficient triangle-counting algorithms, and models for online social networks. The last decade has seen an explosive growth in research on complex networks, ranging from the web graph, to online social networks, to protein–protein interaction networks. Such research has been of great practical importance and has also pushed the frontiers of pure mathematics. One of the goals of the 2010 workshop was to present current research on the theory and applications of complex networks. The papers presented in this special issue should stimulate new and exciting directions in research on complex networks. We would like to thank the authors and reviewers for making the special issue a reality.
{"title":"Introduction to the Special Issue on Algorithms and Models for the Web Graph","authors":"A. Bonato, Ravi Kumar, D. Sivakumar","doi":"10.1080/15427951.2012.635562","DOIUrl":"https://doi.org/10.1080/15427951.2012.635562","url":null,"abstract":"This issue of Internet Mathematics includes a selection of papers that were presented at the Seventh Workshop on Algorithms and Models for the Web-Graph, WAW 2010, held at Stanford University in December 2010. The papers in this issue, unlike the conference proceedings of the workshop, do not have page limits and contain full versions of proofs and algorithms. All the articles have been thoroughly reviewed in accordance with the usual high standards of Internet Mathematics. The papers address a number of topics related to complex networks such as network-creation games, applications of PageRank, efficient triangle-counting algorithms, and models for online social networks. The last decade has seen an explosive growth in research on complex networks, ranging from the web graph, to online social networks, to protein–protein interaction networks. Such research has been of great practical importance and has also pushed the frontiers of pure mathematics. One of the goals of the 2010 workshop was to present current research on the theory and applications of complex networks. The papers presented in this special issue should stimulate new and exciting directions in research on complex networks. We would like to thank the authors and reviewers for making the special issue a reality.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"8 1","pages":"1 - 1"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2012.635562","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59946542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-02-15DOI: 10.1080/15427951.2013.798601
K. Avrachenkov, Nelly Litvak, Marina Sokol, Donald F. Towsley
Abstract Our goal is to find top-k lists of nodes with the largest degrees in large complex networks quickly. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top-k list of nodes with the largest degrees requires an average complexity of , where n is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use a random-walk-based method. We show theoretically and by numerical experiments that for large networks, the random-walk method finds good-quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random-walk method that requires very little knowledge about the structure of the network.
{"title":"Quick Detection of Nodes with Large Degrees","authors":"K. Avrachenkov, Nelly Litvak, Marina Sokol, Donald F. Towsley","doi":"10.1080/15427951.2013.798601","DOIUrl":"https://doi.org/10.1080/15427951.2013.798601","url":null,"abstract":"Abstract Our goal is to find top-k lists of nodes with the largest degrees in large complex networks quickly. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top-k list of nodes with the largest degrees requires an average complexity of , where n is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use a random-walk-based method. We show theoretically and by numerical experiments that for large networks, the random-walk method finds good-quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random-walk method that requires very little knowledge about the structure of the network.","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":"10 1","pages":"1 - 19"},"PeriodicalIF":0.0,"publicationDate":"2012-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2013.798601","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59947463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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